To study polar amplification (PA), two idealized energy balance models are constructed: a dry-diffusive down-gradient model (diffusion model) and a model where horizontal heat fluxes are configured in such a way as to maximize entropy production (MEP model). The effect of spherical geometry and non-uniform tropopause height is investigated in both models by comparing with a "cartesian model" with flat tropopause in both frameworks, and the baseline temperature anomaly from a decrease in planetary emissivity exhibits tropical amplification (TA). For the diffusion model, spherical geometry has minimal effect on the temperature anomaly, even though the resulting differences in volume is large between the poles and tropics. Similarly, having a non-uniform tropopause height has minimal effect on the temperature anomaly. A non-uniform diffusivity increases contrasts between polar and tropical regions, and may contribute either to PA or TA depending on which parameter is perturbed. All of these aforementioned contributions to the temperature profile are shown to be represented by "advection" velocities. In the MEP model, geometric considerations are shown to be irrelevant for the calculated heat transport. PA is found to be affected by polar albedo decrease, which is well known, but also another hitherto unexplored mechanism, that of tropopause height increase (THI). Increasing the tropopause height uniformly yields a polar amplified temperature anomaly in all diffusion models. This effect is dependent on the magnitude of the diffusivity in the models. A comparison in Polar Amplification Factor (PAF) to albedo decrease is made for realistic values, and in the diffusivity range 10^6 m^2 s^(−1) – 10^7 m^2 s^(−1) THI yields comparable magnitudes. A study in asymmetries between the Arctic and Antarctica is also made, and it is found that while the elevation of the Antarctic continent (H ≈ 2500m) should increase the warming effect of THI, the assumed lower diffusivities there restricts this heat transport. Finally, analytical results from the maximum entropy production (MEP) model suggests that the effect produced by THI may be counteracted. A suggested mechanism for this is that of simultaneous diffusivity decrease.