all the 68K CPU's run hot in my experience. you could easily melt some cheese on them. The 68040 could easily fry some bacon and eggs.
Agreed, it depends on each person's subjective view of "hot".
I am left wondering if op is going to have a shot at removing the battery and cleaning the leakage or send the card off for repair. It's a decision only he can make but if I were in his position I'd definitely like to get that leakage cleaned first as it's plausible that it's causing the issue with his card and after a bit of attention all could be well. It's worth a shot in my view: the current state of the card is "broken" anyway and this is a repair attempt that will cost a small amount of money for supplies plus a little invested time.
His A1200 tower & mediator setup is very similar to my own, but I have the Blizzard accelerator card rather than Apollo.
Anyway, good luck AmiBoy!