A filtered neutron beam technique has been used to measure changes in an average total neutron cross section of tin. The cross section was averaged over a neutron energy band from 23.1 to 24.9 keV, which covers a number of resonances. This average cross section, when measured for a sample of intermediate thickness, shows the effect of Doppler broadening of the resonances. The effective average total cross section increases as the temperature of the sample increases with a change of slope at the gray-to-white tin transition and a step at the melting point. The changes of slope and steps are evidence of changes in the thermal motions of the tin atoms in the sample when the sample changes its physical state.