The impact of thermo-optic refractive-index changes arising from the core heat load in a dual-core fiber amplifier is studied through finite-element based numerical simulations. Trends in coupling lengths, effective area, core overlaps of fundamental and higher-order supermodes, effects of asymmetric heat loads, and thermo-optic mode coupling parameters are quantified. It is concluded that the coupling between cores is only moderately altered by the overall heat load, but can be strongly sensitive to asymmetric loads. The influence of the core coupling strength is demonstrated to be very important on the supermode effective area, besides the shrinking due to thermal effects. While the thermo-optic index perturbations can lead to guidance of higher-order supermodes, it seems realistic to maintain single-mode operation through gain suppression of the higher-order modes. On the other hand, thermo-optic couplings between fundamental supermodes are found to be quite strong.