I tried something that has worked very well, not only for radishes but mustard greens and turnips too. I planted in an area near two very large trees ... gets good sun in the morning before it gets scorching hot, then an hour or two of shade before noon. Then sun for an hour or so around noon and then filtered sun for the next couple of hours. By the time that the sun is direct, it is late afternoon and the sun is pretty low and not scorching.
Additionally, I water lightly every day. The radishes are beautiful and just the size they should be -- they are crisp and mild. We had turnip greens with diced turnips last night and they were also mild.
Everybody and their brother told me that I couldn't grow radishes and greens at this time of year that would be worth a darn. I was tickled to be able to provide them with some that they enjoyed, and it has averaged 95 degrees a day for the last 3 weeks.
That makes sense in hot areas. I replanted radishes a couple of weeks ago and they are all tops so far and I’m trying to keep the top 4 or 5 inches of the soil damp. I gave up on Turnips due the root maggots burrowing in the pulp but I should try again using Remay row covers to keep the fly from laying it’s eggs.