To be fair, I haven't actually played with the mod yet as I'm waiting till I finish with university work to dig into some hardcore Rimworld. That said, I've watched a few playthroughs that use this mod and have used the shield generators.
It seems that they almost always burst into flames as soon as fired upon, which seems a bit excessive to me. Most players seem to counter this with fire-foam poppers, but that seems like an unnecessary and/or unintended extra resource cost for something that's clearly endgame and seems to be already balanced around its power usage.

My actual question is this: Is there any good ways to prevent them from bursting into flames? Can I just place them in a fireproof room or will the generator itself burn away? Can I put one in a heavily cooled room to prevent it from overheating? Should I just lock a pawn in a room with one to beat out any fires that start?

If none of those options work, and indeed if any of them do, I have a few suggestions that might help to make them more reasonable to use.

1) Make the generator itself fireproof (if it isn't already). This would let you place one in a fireproof room and just let it 'burn' without actually causing any harm. If you don't, the fires can still hurt nearby pawns or items, so there's still a tactical choice to be made. It forces some extra resource expenditure to make the room, and extra cooling if the room is inside your base, but it's not an ongoing resource cost.

2) Fire-foam/water/fire suppression turrets. Basically the fire extinguisher from more weapons mounted on a turret. This would just be an awesome addition whichever way you look at it. Ideally they would act like the floor turrets and only pop up when a fire is nearby, but normal turrets that spray fire-foam onto fires to put them out would be a useful addition for any base AND solve the shield generator fire issue. They could even require a special fire suppressant made from chemfuel or neutroamine to reload. Or just water, which seems to be counted as a non-cost in vanilla, in which case I'm not sure what the reload material would be.

3) Reusable fire-foam/water sprayers and/or firefoam/water grenades. Think a shorter-range fire-foam popper that can be easily rearmed like a bear trap. Something like the ceiling water sprayers you see in office buildings. Again, they would be cool in any base, and would make fire suppression a bit easier in general. For the shields it would basically be the fire-foam popper method but with the ongoing resource cost removed.
Water could be a less effective version of fire-foam, and would allow tribal-level fire suppression devices, things like a suspended sack of water over an area or a bucket of water that a pawn could equip as a 'grenade' and throw to put out fires.

4) Have them just produce heat without actually starting fires normally. There would have to be a special case for when is placed outside (perhaps current behavior), but allowing them to be used more effectively the more dedicated cooling they have would be pretty neat.

5) Only set fires/overheat if the shield is actually broken, and have a fail-safe setting that disables it if it is going to break soon. That would make you choose between soaking a few extra shots and risking a fire, or letting your colonists get shot up a bit extra.