The cool of the evening. Many people take a walk after dinner as the sun is going down.
I myself love walking/jogging late at night but I'm a guy so the dangers for me are less (even so I do take care...carry no money, have a phone and stay on main well lit roads).
This morning I had an 80 minute jog at 5:30am before the bite of the sun and the flys set in. It was very pleasant.
You may wish to get some lycra style gear to wear. It is light and thin so sweat evaporates quickly and keeps you cooler.
I'm no fan of jogging or walking in the heat but sometimes I do it just because it is hard
That means setting your mind to the task and toughen it out. I keep in my head that this session will do me the power of good. Motivate from within...what doesn't destroy me makes me stronger (and thinner).