The basic premise is about a metahuman whose skin always emits large amounts of heat. It's usually around 300-500 F (150-260 C) degrees, but when he gets mad, in pain or in a serious fight, it can reach temperatures of 3000 Fahrenheit (1650 Celsius).
My question is what could he do to get around this problem or cover it up.
Any thoughts, questions or ideas would be greatly welcomed :)
The first thing you have to worry about is feeding him.
To generate that much heat, he has to be getting the energy from somewhere. Let's assume that he metabolises energy the same way we do; through food. The average human consumes around 8700Kj to maintain a body temperature of around 37oC, in environments that average around the 25oC mark. Note, this is a MASSIVE simplification, but will help with rough order of magnitude figures.
That means that every day, the human body is using around 725Kj per degree C to maintain the differential. When we do the math, let's make it easy on ourselves and say that the average body temperature our hero maintains is 325oC, or 300o above room temperature. That means that our hero would need to consume 217,500Kj of food each day. He's going to spend all his time eating, and that's not the half of it; he's going to need massive lung capacity to metabolise the food with oxygen, and his biggest problem is going to be getting enough water given that it's going to flash boil as he tries to drink it.
Another problem that you have is that trying to insulate yourself so you can touch others is a REALLY bad idea. With that kind of warm blooded metabolism, even some form of lead lined insulative clothing including shoes and gloves is only going to amplify the problem in that the body can't dispel the heat through normal convection. That means that your body temp is going to climb rapidly, potentially melting down the insulative material and overwhelming it.
Even if he did find a way to have a meaningful and intimate relationship, he can never father children. I always wondered why (not to be indelicate) something as sensitive on the male body like testes were put out in the open so to speak, rather than being more protected inside the body. That is, until I read that male sperm is actually quite sensitive to normal body temperatures and actually start to die off at 37o; presumably this is so that women can't ovulate and be fertilised by 'old' sperm that may have degraded - you only want the fresh stuff. The scrotum is in effect providing a heatsink for them to keep them cool. The problem is at these temperatures, your hero is effectively sterile regardless.
But for the sake of argument...
Ultimately, the best thing your hero could do is go angelic; Imagine a thermal suit that efficiently takes the heat out to a massive heat sink array on his back that would effectively look like metallic wings. This might allow him to touch people with his hands or be around people to his front, with massive heat radiating out from behind him instead.
This would have two practical benefits; the first is that he could have meaningful conversations with friends in a circle around him so to speak, but it would also prevent anyone from ever sneaking up on him from behind.
Your hero breaks the second law of thermodynamics, and creates more energy than she consumes. Even assuming that he isn't in a government lab, (they gave up on his power as non-reproducible) he's a non-radioactive source of constant heat that has no complex waste products. At 500Fish, he's hot enough to run a powerplant by virtue of his presence: at higher temperatures, which are achievable if he's properly stimulated, things get even better.
Of course, there's the problem of him heating up hotter than practical containment allows for, sometimes, which is, of course, why he's been lobotomized (or sedated permanently). Since he heats up when she's in pain, a low level constant agony would be handy to be able to induce, with an ability to modulate it to increase/decrease how much heat he's putting off.
All in all, being a lobotomized hunk of meat with some kind of subdermal pain inducer for his entire life probably isn't a lot of fun.
The question of whether something actually does melt under heat has to do with time - how fast the heat gets in (conduction), and how much it takes (physical properties like specific heat). However, at a certain temperature and pressure, everything will melt. A body of hot mass at temperatures like the sun will always be a plasma - it simply can't deal with the extra motion to form bonds and stay together chemically.
At 300 degrees Fahrenheit, not too much will be destroyed. Some rather unexpected substances like wood burn quite a bit hotter, but wood accelerates its own heating when it combusts. So it would mostly be about wearing something light enough and heat-taking that would not interact with objects in the environment too much. I would think wearing something insulating, and not metal, would be better if the temperature is always hot. Otherwise, the metal or material that transfers heat quickly would cause, well, embarrassing losses of heat and probably damage to property.
300F is already too hot to do a lot of things, like touch people or anything with some flammability. It's probably too hot to reliably refrigerate on your body, if that's not somehow dangerous for this person (I doubt a home refrigerator could do that, unless mad-scientist Max made it). On the other hand, 3000 degrees Fahrenheit is quite balmy, and if your meta-human has temper tantrums or gets beat up a lot, and for long enough, they would melt just about anything. As a reference, sand melts at 3000 degrees Fahrenheit (into glass), and there aren't any known substances that survive above something like 5000 degrees Fahrenheit for an indefinite time. Many things will vaporize at 3000F, like Aluminum according to Wikipedia. Your metahuman would be a dangerous foe if they weren't sinking into the ocean or melting concrete fast enough.
As an edit, I guess your metahuman could have a sort of flying superhero MO and then not get anything hot except a plume of air above them. The right suit could do the trick, in theory...
At those temps you can't clothe him, so he's always in his birthday suit. And you can't have anyone touch him. When it rains, the water turns to steam as it hits his skin. We'll need to solve that. A carefully manufactured suit (or gloves or shoes) of Aerogel could be used to contain the heat. Aerogel is amazingly heat resistant as well as surprisingly strong. However, it comes with some downsides:
If he can't feed on metal, he's in trouble. Water will steam. Certain types of oil may suffice for liquid, but that's assuming his body can feed on that. As @TimBII mentions in his answer, food (and intimate touch) are probably not on the table unless he feeds on different foods.
If he can't fly, walking on grass is a very bad idea. He won't be able to walk anywhere without heavy metal or aerogel shoes. He will probably have to live in a remote desert location, and be transported when needed. But any ship, plane, car, or other transportation device will need to consider how to move him quickly without destroying the transport.
At that much heat being generated, especially when he's mad, he's basically a walking energy source. All sorts of bad people and governments would design facilities to house him, but collect and use that heat (eg, to make magnesium or hydrogen) or convert it into electricity.
He/she/zer could wear a foil/thermal suit or a refrigeration suit but physics in this sutuation gets fuzzy and foggy. It may actually hurt the metahuman by means of overheating andor melting down.
