We report the experimental realization of a non-galvanic, primary thermometer capable of measuring the electron temperature of a two-dimensional electron gas with negligible thermal load. Such a thermometer consists of a quantum dot whose temperature-dependent, single-electron transitions are detected by means of a quantum-point-contact electrometer. Its operating principle is demonstrated for a wide range of electron temperatures from 40 to 800 mK. This noninvasive thermometry can find application in experiments addressing the thermal properties of micrometer-scale mesoscopic electron systems, where heating or cooling electrons requires relatively low thermal budgets.