Your technician is correct in one way about the cracks, you probably won't detect anything too strange from it unless it starts buzzing. Often that is caused because additional to the cracks, the board separates from the ribs. Still repairable, often by gluing and pinning back to the ribs again, at least to the state it was at with just the cracks. You might notice some sound changes in season changes to higher humidity levels when the cracks close up ( they actually can close right together in warm humid weather when the heat is off).
However, that said, it's up to you if you feel it's worth investing money into a piano with a cracked soundboard which if nothing else, diminishes the value of the instrument even though it sounds ok.
The damage is done but the question remains now, what and how much more damage will there be due to that heat source. It's probably too dry in there, you most likely can hold off to a large degree more damage by increasing the humidity level . Talk with your tech about that as well.
Re pinning is fairly common, they install over sized pins and it works very well as long as the pin block has resilience in it. It too is subject to cracking from low humidity. That you so far have avoided that is a good thing !
Just my thoughts, I'm not the pro though have done quite a bit of piano work over the years.