The temperature of the exosphere cannot be specified. This is because the exosphere layer of the atmosphere is almost a vacuum; the thickness of the air is negligible. Because of this thin air layer, heat cannot be transferred to the air particles even if the air is very hot.
The particles in the air in the exosphere might be hot, but since the exosphere is almost a vacuum, the exosphere would feel very cold. When sunlight falls on the air particles in the atmosphere, they can get extremely hot; however, the particles not exposed to sunlight can be freezing cold.