I have had that problem with push-ups or padded bras. They "insulate" and so retain the heat. Nice in winter, but in summer not so much.
I have some bras that are almost like lingerie that I wear. They are sheer and lightweight. The downside is that they can make nipples more visible, since there is no padding to keep them under control. Wearing a baggy top can hide that, but I have discovered that most people either don't notice or don't care.
While moving, I wore tighter, lightweight tops that were comfortable for the long drive. Perhaps the perception is that when it is hot, it doesn't matter. I prefer to dress more conservatively, but I had no stares, and I was cool and comfortable.
