The first experimental measurements of intense (-7×1019 W cm-2) laser-driven terahertz (THz) radiation from a solid target which is preheated by an intense pulse of laser-accelerated protons is reported. The total energy of the THz radiation is found to decrease by approximately a factor of 2 compared to a cold target reference. This is attributed to an increase in the scale length of the preformed plasma, driven by proton heating, at the front surface of the target, where the THz radiation is generated. The results show the importance of controlling the preplasma scale length for THz production.