Vishay’s application note on zener diode voltage stability. Link here (PDF)
The Zener voltage (VZ) of a Zener or avalanche diode depends on the diode’s junction temperature. Any current running through the p/n junction barrier generates the electrical power of: P = IZ * VZ. This electrical power is equivalent to the thermal power applied to this junction. Depending on the duration and the intensity of the current, the applied thermal energy increases and heats the junction.