I don't know that they're actually asleep, but after they've come out and warmed up then eaten, they usually go back into the hide until evening when they come out again. I've looked in on my tortoises during this resting time and very seldom do I see their eyes closed.
My tortoise sleeps in the warm side, head on the ground, eyes closed! I got really cared when that happened! Then I realized my tortoise loves the heat