In the theory of general temperature modulated differential scanning calorimetry (GTMDSC), the modulated temperature of furnace accords with a random cyclically modulated rule and even a random non-cyclic rule. In this paper, the temperature variation rule of platelike sample in GTMDSC has been drawn with strict mathematical derivation. The obtained analytical result reveals the total variation rule of the platelike sample from its initial equilibrium state to its steady state. With this temperature variation rule, the variation rules of both reversible and irreversible heat flows, temperature lag, internal energy and effective specific heat of the platelike sample have been derived and studied as well. Sinusoidal rule of modulated temperature is only a very special example of general cyclic modulated rules. If the thermal conductivity of the sample is so great that the temperature gradients within the sample can be neglected, in this case the temperature variation rule derived from the fundamental equation of the temperature distribution of GTMDSC is the same as the current TMDSC theories. If the modulated part in temperature equals 0, it reverts to the conventional DSC situation, so all the results in the GTMDSC model derived in this article are automatically suitable for the conventional DSC situation and current TMDSC theories.