Make sure you are well hydrated, and yeah why not lie in a cooler bath if you think it will help cool your core temperature down!
Personally I thrive in the heat! I love it and I am really glad that I am pregnant in the summer lol, I hope you can cool yourself down, just drink lots of water every day, at least 8 glasses they say and I do drink that at the moment otherwise I feel really faint and dizzy.
xx