In magma reservoirs, large temperature contrasts imply large variations of viscosity. We determine the characteristics of thermal convection in the laboratory for viscosity ratios of up to 106. In a fluid layer cooled from the top, convection develops below a stagnant lid. Plumes generate temperature fluctuations whose magnitude, θmax, is proportional to the temperature contrast across the unstable region, ΔTe. Scaling analysis and experimental data show that both temperature scales depend solely on the local function describing the variation of viscosity µ at temperatures close to that of the layer interior, Tm, and are equal to: In the Makaopuhi lava lake (Hawaii), temperature fluctuations were recorded below the growing crust. For the viscosity function of the Makaopuhi magma, their magnitude is predicted to be 18°C, in agreement with the observations.