A stone yes. A thick stone wall. Absolutely not. Same principal applies for not using your super sharp steak knife on a stick of butter. The butter is too thick and will cause your steak knife to bind.
I've seen a katana cut a golem in half before. I've seen one cut through an airplane, engine block and all. This is standard convention for impossibly sharp swords, seen in countless shows and video games.
The only time I've ever seen a fire elemental that was
remotely susceptible to fire magic, it was in World of Warcraft, and there was significant critical backlash about how ridiculous it was (which was subsequently ignored, as those players moved on to other games). The normal,
expected effect of heating up a fire elemental is
nothing; or, depending on the game, it might be
healed. Regardless of what rationalization you try to apply here, it simply doesn't conform to the standard fantasy logic that everyone expects, and in deviating from that it hurts immersion as players have to second guess what they always thought they knew.
I'm not saying that you shouldn't do it, if you really care more about game balance and you don't want your pyromancers to end up not contributing for an encounter, but be sure that you know your audience before you include such changes at your table.