The effect on plasma measurements at high pressure of the thermal sheaths in front of plane cooled probes is discussed both for stationary and flowing plasmas. In stationary plasmas, the measured electron energy would be dependent on the probe temperature owing to the losses in the thermal sheath. A critical review of some of the earlier experimental work with cooled probes shows the limitations of the stationary analysis since most high pressure and high temperature plasmas are flowing plasmas. It is suggested that in flowing plasmas the cooled probes give reliable results for electron energy owing to the dependence of the thermal boundary layer thickness on the distance from the leading edge of the probe along the flow direction. An order of magnitude estimation is made for the thermal layer thickness of a low gas flow argon arc at atmospheric pressure. The normal use of highly negative cooled-probe data for charge density measurements is reasonably accurate both for stationary plasmas and for flowing plasmas where the probe surface is aligned along the flow direction. However, in flame and alkali-seeded inert gas plasmas, the probe current would become dependent on the cooled probe temperature owing to the influence on the thermal ionization process in the vicinity of the probe.