The temperature dependence of the capacitance of very high efficiency silicon heterojunction solar cells exhibits an anomalously large increase with temperature that cannot be explained under the usual depletion approximation. Based on a full calculation of the capacitance, we show that this large increase of capacitance with temperature of p-type hydrogenated amorphous silicon (a-Si:H)/n-type crystalline silicon (c-Si) heterojunctions occurs when a strong inversion layer at the c-Si surface appears. It is further shown that due to the promotion of inversion as the temperature increases, the temperature at which strong inversion appears depends on the valence band offset and position of the Fermi level in a-Si:H. Therefore, a simple analysis of the temperature dependence of silicon heterojunction solar cells' capacitance can be used to reveal the presence of a strong inversion, to study details of the band diagram and to get insight into the heterointerface.