Data presented here deal with the measurement of a two-stage Gifford-McMahon cryocooler dynamical thermal response to programmed square wave and sine wave power inputs around 4 K. Square response data report the raw temperature data points measured by the sensor. Properly filtered data are also presented and results of exponential decays fitting analyses are shown as well. Sine response data were acquired with two different experimental setups and at several frequencies; data report the frequencies of the input stimulus, the measured temperature variation and the phase between input and output signals for both setups. More details about the experimental background can be found in the related research article, “Experimental analysis of the thermal behavior of a GM cryocooler based on linear system theory” (Sosso and Durandetto, in press).