Temperature Cycling Test is performed to determine a product's or component's ability to resist extreme temperature variation; typically ranging between -40C and +125C at a rapid ramp rate.

References:

JEDEC Standard JESD22-A104B

Mil-Std-883G, 1010.8 (A, B, C, F) 

Power and Temperature Cycling (PTC)

Similar to Temperature Cycling Test with power cycling:

Typically, this test is selected at its normal operating conditions where the device is subjected to high temperature excursions and is required to power on and off at all temperatures.

This test is performed to determine the ability of a device to withstand exposure to such temperature extremes with operating biases periodically applied and removed.

References:

JEDEC Standard JESD22-A105