The dc electrical conductivity of high purity, polycrystalline alumina has been measured during exposure to 60 kV peak X-irradiation and 20 MeV proton irradiation at temperatures up to 700°C. In the absence of radiation the conductivity was found to have an activation energy of 0.30 ± 0.01 eV below ∼ 280°C and 1.41 ±0.01 eV at higher temperatures. Under irradiation the apparent activation energy was reduced to 0.06 ± 0.01 eV at low temperature and varied with the type of irradiation at higher temperature. The radiation-induced conductivity was found to follow a power law with dose rate in which the dose rate exponent, δ, varied in a complex manner with temperature. With X-irradiation δ was approximately unity at low temperatures, then fell to a minimum of 0.7 at ∼ 225°C, after which it rose to an intermediate value. Under proton irradiation the dose rate dependence was supralinear with δ = 1.25 up to a temperature of ∼ 500°C after which it fell to a minimum of 0.58 at 630°C before increasing to become supralinear again at higher temperatures. It is proposed that the supralinear behaviour during proton irradiation follows from displacement damage creating aluminium vacancy centres which behave as hole traps with an extended density of states within the band gap.