Temperature is a property that determines the direction of spontaneous heat transfer between systems placed in thermal contact.

If two systems can exchange energy as heat, energy flows spontaneously from the system at higher temperature toward the one at lower temperature until they reach thermal equilibrium.

Zeroth law of thermodynamics

If system $A$ is in thermal equilibrium with $C$, and system $B$ is also in thermal equilibrium with $C$, then $A$ and $B$ are in thermal equilibrium with each other.

This transitive relation is what makes temperature a meaningful measurable property and allows a thermometer to compare systems.

Temperature scales

Absolute temperature is measured in kelvins. Temperature differences in kelvins and degrees Celsius have the same numerical size, but their zero points differ:

$$T_{\mathrm K}=T_{^\circ\mathrm C}+273.15.$$

Microscopic interpretation

For systems in thermal equilibrium, temperature is connected statistically to how energy is distributed among microscopic degrees of freedom. It should not be identified simply with the speed of one individual molecule.

Temperature describes a macroscopic state; heat describes energy transferred because of a temperature difference.