Hot climates

I have been wearing hobibear barefoot shoes to work, out, and to walk.

My concern is I live near Phoenix and would like to start running some. But, the times I can run at night the road is still quite warm. Plus the trails are very dry and rocky.

I am wondering what do you guys wear for something like that? With trail running shoes it’s no problem. But, with minimalist shoes I wonder if it would be better to go with 0 drop altras. Or what do you guys wear?