I would not trust any claim made by fish-street. They have been known to stretch the truth a lot. (they once claimed they are selling a newly designed power supply they designed themselves, but it is actually your generic cheap laptop power supply, like the ones that comes with JCT pumps now) That probably means the stock controller is not capable of running 100% and the new device they are selling can, in order to promote the sales. The other possibility is, I know the stock controller uses P-Channel N-channel mosfet pairs. This is not as efficient as using N-channel mosfet pairs. So perhaps the T1 is using N-channel mosfets only. The green board is using all n-channel mosfets.
All you need to do to maximize this is make sure pin 16 of the motor controller chip gets the max 5v. You can try putting on voltage higher than 24v, but I don't think that is what the fish-street controller does, as you still use your stock 24v power supply. I doubt there is any voltage boost Applying a higher voltage may risk burning out the motor coils.
If it is getting hot, then using a heat sink makes sense. I know I found a heat sink on ebay specifically designed for these boards, but can't seem to find it now. I should have bookmarked it.