I want to create a sapient, amphibious species who have developed a civilization around as advanced as late bronze age Egypt and the Middle East. I would want to know if these sapient amphibians could be able to develop metallurgy or if their skin would be too sensitive to heat to smelt metals.
If they can manage being around fire metallurgy won't be much more dangerous than staying close to a fire.
In our own development, we have managed to control fire way before reaching the bronze age, already in the stone age, and that's probably what kicked us on the sapience way.
And our skin is not that sturdier when it comes to handling radiant heat or spillage of molten metal.
As long they find a way to keep it moist, they will find a way.
On a side note, one can get somehow used staying close to hot surfaces or flames: ask most of the moms or cooks who spend their time cooking.
They absolutely could.
Let's assume we are talking about something like an anthropomorphic amphibian, meaning something that is anatomically very similar to a human.
While generally amphibians are more susceptible to heat than we are, there are some that can do pretty well in hot situations (for a limited amount of time). So a lot would depend on a genetic predisposition.
Early smelting practices suggest that ores were probably smelted in shallow pits. Archaeologist are still debating about this, but some think the draught to raise the temperature may have been achieved through the wind. If that was the case, you wouldn't really need to stay close to the furnace for long, which makes it much more likely for an amphibian sapient specie to be able to smelt.
There's a couple more things that would help.
The first is, as already pointed out by others, clothing. That's what we use to reduce our exposure to heat, and it's likely what they would use too.
The second is proximity to water. It's very likely for a sapient amphibian specie to build their facilities and villages in very close proximity to water. Being able to take a few steps away to submerge yourself in water would greatly help. Not sure how practical this would be, but they could even try to do most of their work while partially submerged (think a shallow pool or something), which would reduce the dehydration rate.
So in conclusione, while probably not their favorite task, smelting and metallurgy could easily be something they would do.
Hands (which imply opposable thumbs and bipedalism) and large brains are what you need for civilization and metallurgy.
Whether your amphibians can evolve into sapience depends on how closely you adhere to the terrestrial definition of amphibian.
There is no reason why being amphibious would impact there ability to smelt metals. If they are specifically lissamphibians, then that may effect their smelting, though not because of their skin. The actual problem with a lissamphibian smelting is the fact that they are generally simpler than other types of life. This means that they have less access to oxygen, which may limit their intelligence, and may also lead to them being smaller, which will make it harder to manipulate fires