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We study the electronic thermal conductivity κ el and the thermal diffusion constant D Q,el in the square lattice Hubbard model using the finite-temperature Lanczos method. We exploit the Nernst-Einstein relation for thermal transport and interpret the strong non-monotonous temperature dependence of κ el in terms of that of D Q,el and the electronic specific heat c el . We present also the results for the Heisenberg model on a square lattice and ladder geometries. We study the effects of doping and consider the doped case also with the dynamical mean-field theory. We show that κ el is below the corresponding Mott-Ioffe-Regel value in almost all calculated regimes, while the mean free path is typically above lattice spacing. We discuss the opposite effect of quasi-particle renormalization on the electronic heat and charge diffusion constants. The calculated Lorenz ratio differs from the Sommerfeld value. We present results for the anisotropic marginal Fermi liquid model and discuss the results in relation to experiments on cuprates.