We report an investigation into a double metal tungstate Raman laser when pumped at elevated average powers. Potassium gadolinium tungstate (KGW) was placed in an external cavity configured for second-Stokes output and pumped at pulse repetition rate of 38 kHz with up to 46 W of average power. For output powers above 3 W, we observe preferential excitation of Hermite-Gaussian transverse modes whose order in the X1' principal direction of the thermal expansion tensor scales linearly with Raman power. We deduce that strong astigmatic thermal lensing is induced in the Raman crystal with a negative component in the X1' direction. At maximum pump power, 8.3 W of output power was obtained at a conversion efficiency of 18%.