We describe ways in which one can test the idea that the temperature parameter relevant for the description of the thermal-like emission spectra observed in hadronic collisions is related to the very large transverse relative acceleration that occurs between projectile and target in the course of these collisions through k T = a/27r. As a consequence, the typical temperature should increase with a decrease in the typical impact parameter, and also significant fluctuations should occur in the temperature, on an event-byevent basis. We perform the first analysis of data to look for such fluctuations, and we find an indication that they are present in antiproton annihilation reactions.