This my first time doing this quest so I'm not sure if it can bug on you. I looked it up online but didn't find anything. I put the stone in the first convector and everything was fine but the next 2 I tried wont work.

The wiki does day that it can bug out. I just did it and had no problems (PC version). You're applying the spell for a while? It takes maybe 10 seconds of heating.

On the 2 I tried and failed I cast the spell on them for several minutes.

You're not trying it in the same convector, are you? It says you have to go find another one for every stone ...