The theory of air-temperature measurement at pressures between 1000 mb and 1 mb is discussed on the basis of the classical approach to heat-transfer problems. The theory so developed has been checked by measurements on ventilated and unventilated thermometers in a bell jar in which the pressure can be varied over the range of interest. The bell-jar experiments support the theory and indicate the way in which temperature-measurement errors may be evaluated under all possible conditions for thermometers in the atmosphere. Finally, a series of flight tests with thermometers of new design, as well as the conventional thermistors, verifies the prediction concerning thermometer errors and indicates the type of thermometer necessary in order to minimize these errors. The flight tests show, in addition to verifying the predictions concerning radiation and time-constant errors, that boundary layers from the balloon, equipment and associated lines may introduce errors at least as great as the systematic errors in the temperature measurement. The flight tests also show the configurations required in order to minimize the errors due to the warming or cooling of the air by the equipment and by the balloon.