Convective Available Potential Energy (CAPE) is the driving force for thunderstorm development. CAPE is closely controlled by wet bulb temperature. The lightning activity measured by a network of ten lightning flash counters widely distributed across continental Australia was studied as a function of wet bulb temperature. At each of the stations, the monthly total of lightning ground flashes, N, increased sharply with the increase of the monthly mean daily maximum wet bulb temperature, T-w,T-max. The dependence was strongest in the tropics and became less pronounced at temperate latitudes. In Darwin (latitude 12 degrees S), the lightning ground flash activity increased by over three orders of magnitude over a 7 degrees C range of T-w,T-max. The corresponding increases for Coffs Harbour (latitude 30 degrees S) and for Melbourne (latitude 38 degrees S) were about one and a half orders of magnitude and about half an order of magnitude, respectively, each over a 10 degrees C range of T-w,T-max. Power law approximations were derived for each of the ten stations and showed that the logarithm of N was directly proportional to the power, P, of T-w,T-max. The value of P showed a sharp exponential decrease with increasing latitude away from the equator.