The temperature measurements taken with the NATE experiment on the Atmosphere Explorer-E satellite during 1977 and 1978 are used to obtain the horizontal two-dimensional distribution of the thermospheric nighttime temperature maximum between latitudes 19.8 deg. south and 19.8 deg. north in the altitude range from 250 about 370 km. Since the satellite orbital period is short in comparison with the Earth's rotation, the local time variations observed are equivalent to longitude variations. Thus, the measurements may be used to study the horizontal distribution of the temperature in latitude and longitude. The data are used to generate temperature maps for the four seasons. The maps show that the nighttime temperature maximum often occurs first at the geographic equator, and shows a tendency to be largest there. A seasonal rotation of the distribution of the maximum is observed in which the maximum occurs in the summer hemisphere before it occurs in winter. The summer maximum is significantly larger than the winter maximum. The local time of occurrence of the maximum in either hemisphere shows an annual oscillation about local midnight with an amplitude of about 3 hours. The observations indicate that the nighttime temperature oscillates with higher frequencies and amplitudes in the summer hemisphere, thus suggesting that the semidiurnal and higher order tidal modes are stronger in that hemisphere.