We theoretically investigate charge transport through serial double quantum dots (SDQDs) with strong electron correlations using nonequilibrium Green's function techniques. In the linear response regime, we compute the charge stability diagram and analyze the Coulomb oscillatory tunneling current, revealing both thermal and nonthermal broadening effects on the current spectra in relation to two gate voltages. In the nonlinear response regime, we focus on tunneling currents in SDQDs under the Pauli spin blockade (PSB) scenario. We find that current rectification with negative differential conductance is significantly degraded as temperature increases, making it challenging to distinguish between the inter-site spin triplet and singlet states. Notably, we observe a robust reversed tunneling current that remains stable against temperature variations, provided the resonant channel in the PSB scenario is coupled to the states of the right (left) electrode, which is fully occupied (unoccupied) by particles. This characteristic provides valuable insights for designing transistors capable of operating over a wide temperature range.