i actually know the answer. The air temples werent just at the top of unreachable mountains. There were some paths that you could take to reach it. The reason the fire nation couldnt just charge up the paths and take over the temple, was because the air benders could defend well against them. However this was fixed when sozens comet came and all firebenders gained major power ups. So with superior powerups, and greater TRAINED numbers, the milatary force of the fire nation was able to beat the peaceful NOMADIC unorganized air benders.
Also the fire benders may have had the element of surprise.
This should answer your question