I have an alien race that can emit beams of heat from their eyes. Is their any way this can be produced by means of a highly evolved organ? If so, how would this organ work?
Glowing eyes of any kind pose a challenge. The best I can come up with would be if the retinal pigments could double as bioluminescent molecules. The creature could in theory make a beam of light shoot out of their eyes, focused by the internal optics of their eye, but it wouldn't be much brighter than a laser pointer.
If you just want heat-beams, but don't really care what orifice it comes out of, then one possibility is that the creature could have a very high body temperature, and they could open up a large pore that is filled with blood vessels to conduct their body heat to the inner surface where the Infra-Red rays can be reflected outwards. This could make the victim feel pleasantly warm. (The trouble is that you can never make something hotter than the source of the rays. Unless your creature has molten lava running through its veins, it won't be able to release meaningful heat.)
If you just want "monster that shoots heat", you could go the chemical route and make them like the Bombardier Beetle, and squirt out violently reactive chemicals. You can get creative here and give them napalm-spit if you want. Or maybe some FLAMETHROWER EYES!!!
Any warm blooded organism produces IR light, peaked at the wavelength of a black body at the temperature they have.
Since the local temperature is proportional to the blood flow and metabolic activity, if you want to have an higher temperature (and an higher emission) you should somehow increase the local blood flow and temperature. Think of a highly vascularized sector of skin, placed above a muscle which can shiver/contract on command to produce heat.
However such emission would be omnidirectional and non coherent. I hardly imagine it as an IR light shining on something, it would be more like a glow.
Okay, so heat is basically atoms moving around a lot and the more they move the hotter it gets. If you want your aliens to actually shoot beams of heat, its just not going to work. The heat would disperse according to the inverse square law so anything further than a few meters is going to be 100% safe because your going to melt you eyes off before it gets that hot.
What I assume, is you basically want laser eyes, like super man but actually based of physics. Firstly I want to direction you to this Wikipedia article https://en.wikipedia.org/wiki/Laser_construction . What your going to have to do is basically make a laser inside the skull of your alien which is going to be hard, but you might be able to get around it.
I can't really give you any tips, because I know next to nothing about this, but atleast you can start on your own research.
A beam of light can never heat something hotter than the surface of its source, so remember that when deciding how hot the beams are.
Anyways, I would give them a bioluminescent gland that produces a hot bright light, perhaps one that's wrapped in heat resistant deposits , and uses a modified eye lens to channel the beam.