Living in Texas, I only go out in the day time during the summer months when I must.
But I put a towel in the freezer and put it over my shoulders or my head when I go out. It is not stylish and some people look at me but who cares when it is 100 F.
Of course, you may not have a freezer large enough to put a towel in it. You can put the towel in the refrigerator assuming that you have one.
Carry a plastic bag with you to put the towel in when you are not wearing it, keeping it in your tote bag.
It will be defrosting as you walk in the heat so water will be dripping on your clothes.
Wear llght colored clothes. Avoid wearing colors like black or navy.
Bring a refillable water bottle with you and drink water all day long.
As Rick says, heat is not just very uncomfortable. it can be dangerous.
Depending on where you are sightseeing, go out very early mornings, evenings and the nighttime. Try to be indoors during the hottest parts of the day or at a pool or beach.