We present measurements of the electron temperature using gate-defined quantum dots formed in a GaAs 2D electron gas in both direct transport and charge sensing mode. Decent agreement with the refrigerator temperature was observed over a broad range of temperatures down to 10 mK. Upon cooling nuclear demagnetization stages integrated into the sample wires below 1 mK, the device electron temperature saturates, remaining close to 10 mK. The extreme sensitivity of the thermometer to its environment as well as electronic noise complicates temperature measurements but could potentially provide further insight into the device characteristics. We discuss thermal coupling mechanisms, address possible reasons for the temperature saturation and delineate the prospects of further reducing the device electron temperature.