Thermo itself...no. Leak... yes. I understand you are indicating that engine heat (higher rpms) expands "something" causing a loss of fluid. Yes, knowing the mileage could be helpful. Yes, as RJ mentioned, no coolant on the ground or elsewhere in the engine bay, could very well lead to a head gasket. FWIW First thing I would do? I'd pressure test the coolant system. (PS One item sometimes overlooked is the radiator cap itself leaking and evaporation being a loss of coolant cause.) Good luck.