The temperature of a system determines that the system is in thermal equilibrium with other system or not?
If a body is at 850 C, it will be 850 C, whether measured by mercury in glass thermometer, resistance thermometer or constant volume gas thermometer.
If X is the thermometric property, let us arbitrarily choose for the temperature common to the thermometer and to all systems in thermal equilibrium with it the following linear function of X :
Θ(X) = aX
Where,
a = arbitrary constant
Two temperatures on the linear X scale are to each other as the ratio of the corresponding X.