Using a random tight-binding model within the coherent potential approximation, the effects of boron and nitrogen doping on the temperature dependence of the specific heat of semiconducting zigzag carbon nanotubes are studied. It is shown that the electronic specific heat capacity behaves anomalously when the temperature is lowered. The presence of this anomaly is clarified on the basis of the idea of the so-called Schottky anomaly. More importantly, in the presence of dopants, the position of this anomaly moves towards higher temperatures and its height shifts down as the dopant concentration is increased. Such behavior is attributed to the substantial modifications in the density of states.