Exercising when it's hot

I am very early into my first trimester (about 5 weeks) and need some advice on exercising at this stage. I've been working out so I know it's okay to continue, but I live in Phoenix and it's July/August (all the rumors are true - it's miserable). There's no way to workout without getting hot (my gym is poorly air conditioned). I've been experiencing pretty significant bloating so I'm trying to walk at night to help, but it is still over 100 when it's dark. Should I be worried about overheating at this stage? I don't want to stop working out now for fear I won't be able to pick it back up once it finally cools off (around October).