We visited this desert in the month of april. Overall you could say the best time to visit are our wintermonths november to april. The place is considered the hottest place on earth, measured by Nasa. They registered 70 degrees celcius in our summer!
The desert is inhabited with several smaller villages. Buy enough water there. The biggest attraction are the sand hills in combination with the building like structures of stone, made by erosion of the wind. From a distance the stones look like buildings, that is where it gets it name from Dasht -e- Kalut means "City of stone". We took a tour with Ali and Shiva from www.visitkalouts.com. They take you for a whole day or 2 days, depending on your time and budget. We walked for some hours to reach a point from where we saw a spectacular sunset. After that we drank tea and watched the stars lying on a carpet in the desert. No other visitors there, so we felt private and enjoyed every minute of this beautiful trip.
Nearby the Salt river (Shur river and the funny Camelhills can be visited in the same day). We also were explained about the irrigation system of the qanats, they run under groundlevel, it was amazing to see this in only one day. Very much recommended.