Well ever since I realized how hot my current gambeson is in the heat I have been considering getting a layered gambeson in natural colored linen. I nearly passed out at PA ren faire from being dehydrated and the heat exhaustion.
You know you can mitigate that by drinking water throughout the day? Whenever you've got your body under load (that is, carrying weight it wouldn't normally carry) then you have to take precautions to make sure said body can continue to function throughout a given period of time. Drinking plenty of water, as well as upping your caloric intake, at least for that day, will help quite a bit in keeping such things manageable.
I should also add, sugary and/or alcoholic beverages will actually make it worse, so sucking down soda, ale or hard cider's not going to help in the long run.
Lies and blasphemy! Do you know how much Coke and Jolly Rancher soda was consumed by Sir Nathan and I this year at VARF? I think I spent most of the day in full harness, with a few "take off the cuirass" cheats on a day or two. You know what's a primary ingredient in sodas? Water! So if you aren't getting enough hydration, drink more soda, since it means more water from that soda.
OK completely sarcastic on that. Kinda. Sir Nathan and I did kill a number of sodas those two weekends and the weather was moderate compared to the 95* weekends we usually had.
I function great with soda / sugary stuff while in armor and heat... so long as that intake continues. An hour or two after I'm out of armor and haven't had soda? Mild headaches to outright migraine, and I get moody. But I'm built like a mule so I handle the weight fairly well. I do suggest following Sir William and Sir Ian's advice about more water.
If there's anything that breathes less than modern quilted padding, it's plate armor, and I'm quite familiar with that "I'm baking from the inside out!" feeling. If you're getting dehydrated, you're doing it wrong; if you have to pee, you're doing it wrong. Find that moderate spot.
But don't let it sway you from buying another gambeson too.