An experiment to heat the lower ionosphere by irradiating it by a. 40 MHz transmitter shows an apparent cooling of the ionosphere below 90 km altitude. Considering the interaction of the radio wave with the ionospheric electrons cooling would hardly be unexpected. This apparent paradox, is explained using a two fluid continuum theory of incoherent scattering which includes unequal electron and ion temperatures. This analysis demonstrates the expected heating and permits an electron density and collision frequency profile below 100 km to be obtained. The results are obtained using a library of contour plots prepared for this purpose. The library will be useful in future experiments.