The phonon drag and electronic diffusion contributions to the tensor M which determines the heat flux U=M.E is calculated for a two-dimensional electron gas in a perpendicular magnetic field B. The drag component is obtained using Boltzmann transport and diffusion is included using the lowest-order cumulant approximation to describe scattering between Landau states with different orbit centres. The 2D Landau levels have Gaussian model lineshapes with RMS width gamma =CB^1/2 which is the only adjustable parameter. At temperature T=5.02 K, drag dominates the predicted M_yx(B) values which are in good agreement with new data for Si MOSFETs taking C=0.6 meV T^-12/. The calculated M_xx values are in worse accord with the data because the predicted drag contribution M_xx^g is zero. Both M_xx and M_yx reveal magneto-oscillations originating from fluctuations in the density of states at the Fermi level. The authors show that at T=5.02 K, setting M_xx^g=0 has little effect on the accuracy of the magnetothermopower S_xx(B) but yields poor approximations to the off-diagonal term S_yx(B). At T=1.47 K, these thermopower components are diffusion-dominated. The predicted values are comparable to experiment although the magneto-oscillations are overemphasized in S_yx and underestimated in S_xx.