The dependence of proper temperature on cylindrical coordinatesT0（ρ）in thermal equilibrium of a fluid system on Einstein turntable is solved by special and general relativity separately. The results show that the contraction of motiontemperature depends only on the speed instead of on the acceleration of subsystems. According to uniformity in space and constancy in time of the coordinate temperature of an equilibrium system, the space-time duality between Einstein turntable and early universe directly presents that the proper temperature of a medium of the early universe is inversely proportional to the spatial scale-factor R(t).