They are CFL bulbs so the bulbs themselves can heat up, but they don't radiate heat onto me as I am working. I've never noticed any heat at all so I put my hand up on the softbox covering and they were warm. :)
I do, well, I did until a house fire lol. I do plan to get another when I am able to move back in my house. I like it very much. I use it with my iphone.