I used to drink a can of Slimfast shake after a long run/marathon. Cheaper than specific sports stuff, but has all the stuff you need in it. I struggle to eat after a very long/hard session because I feel sick, but can get one of those down pretty easily.
You might get some funny looks buying it if you are a skinny racing snake. (I'm not....)
It's the training that gives you the "gains", so making sure you refuel afterwards to aid recovery will give you the best chance of making improvements.
Seriously though, I suffer badly in heat too - give me cold and preferably rainy conditions any day. Getting fitter and losing weight does help, but I've been running for 16 years (on and off, had 2 babies in there) and I still suffer.
For training, avoiding it is easier - run early in the morning or late in the evening where possible, or at a push on a treadmill in an air conditioned gym. Racing is not so easy, as they won't change the race time to suit you.....
Loose/cool clothing is good. Wear as little as possible - vest and shorts if you feel comfortable in that, baggy t-shirt and shorts if not. Avoid long leggings at all costs. Wear "technical" wicking t-shirts - cotton will boil you.
If you have long hair - wet it! And keep it wet - at water stations drink some, then pour the rest over your head. It makes a huge difference.
Lastly - make sure you are well hydrated. Drink lots in the week up to an event (or all the time during training in warm weather) - it's not enough just to drink a bit more on the day/during the race. The swelling comes from your body trying to retain fluid so that you have it in reserve for sweat to cool you down, If it's used to you replacing it regularly, it'll "allow" you to sweat, which will cool you down and also reduce the swelling.