Measurement of temperature

The temperature of a system determines that the system is in thermal equilibrium with other system or not? 

If a body is at 85C, it will be 85C, 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


a = arbitrary constant 

Two temperatures on the linear X scale are to each other as the ratio of the corresponding X.