Loss of water

Let me know if what I understand is right, the car has no heat and the temp guage shows cold< then
it runs hot, I would start with the thermastat, it could be going bad, keeping it open then closing causing the difference in the temp. On the sending unit there is a wire, ground the wire and watch the reaction on the temp guage it should go to the hot position, you can have the coolant system pressure checked to see if it holds the pressure. This would tell if there is a leak.