We performed a numerical analysis of 4H-SiC high power Schottky diodes under forward bias conditions. It showed that self-heating processes in conjunction with high current densities strongly affect the device operation. Our device simulations were based on new experimental datafacts for the non-linear temperature dependence of the thermal conductivity K(T) and well-known values for the heat capacity c(T). Both single pulse operation and operation under constant current pulses with a defined duty-cycle were analyzed in detail, and two different device structures were compared with each other.