I could tolerate it too, but would find it unpleasant. The ST just doesn't have that much going for it that I would be willing to put up with the heat. The scenery is pretty blah most of the time with a pretty view only pretty rarely.
It does have a few things going for it, besides being good for a winter tour. It is the shortest and flattest coast to coast ride if that is a plus for you. There is a nice variety of foods along the way (Mexican, Cajun, Barbecue, Seafood) and a lot of interesting people.
That said, I would rate the TA as a much better ride scenery wise and suspect the NT or some route strung together using other ACA routes would be as well. There is nothing on the ST that compares to the beauty of the better sections of the TA at least to my eye. I mostly remember the scenery west of Del Rio as day after day of drab brown land with no water and not much to distinguish one view from the next. There were fairly nice views from the very limited number of passes, but they were a tiny portion of the ride and mostly not all that spectacular.
So, bottom line, I'd highly recommend considering doing the TA or the NT, maybe using some other options like the L&C if you want. On the other hand, if you love 100 F heat and drab brown land you may love the ST in Summer. Apparently some folks do.