In two-dimensional chiral p-wave superconductors, the zero-energy Majorana fermion excitations trapped at vortex cores are protected from the thermal effects by the minigap, Delta(2)/epsilon(F) (Delta : bulk gap, epsilon(F): Fermi energy), which is the excitation gap to the higher energy bound states in the vortex cores. Robustness to thermal effects is guaranteed only when T <>Delta(2)/epsilon(F), where Delta is the bulk gap of the s-wave superconductor.