"Is the weather in Egypt during the month of August unbearably hot? "
It was so hot at the pyraminds in early October when I went that the vendors were doing a brisk business selling hats. Some people put their shirts over their heads and others were using umbrellas for shade. So, yes I think August would be unbearably hot.
"Would September/October be a better time to travel to Egypt?"
Yes, and the later in October the better.