This will be a struggle…
The real undersuit was sharkskin neoprene. That’s fairly tough to find. If you can find a .5mm-1mm smooth skin neoprene that would be your best bet.
It doesn’t matter if you wear neoprene or even Lycra. You are still going to sweat to death. It is the nature of wearing batsuits.
The cowl is the real culprit. The heat just gets trapped in it.
Best thing to do is take breaks. If it is for a convention get a hotel that is attached to the convention center. Every hour go back to the room for 30 minutes.