The temperature of a sample of matter is a measure of the?

Answer: the average kinetic energy of the particles.

Jusitification:

Temperature and heat energy are closely related.

While heat is the kinetic energy of the particles of a substance which is transferred from a hotter substance to a cooler one, the temperature is a measure of the average kinetic energy of the particles in a substance.

The relatively high kinetic energy the particles of a warm substance is transferred to the cooler one by the motion (vibration or translation) of the atoms of molecules. The energy transferred is heat energy.