Theoretical expressions for the photocurrent in Heterojunction solar cells with Intrinsic Thin layer (HIT cells) are derived taking into account tunneling of electrons and holes through wide-bandgap layers of α-Si:H or α-SiC:H. The criteria, under which tunneling does not lead to the deterioration of solar cell characteristics, in particular, to the reduction of the short-circuit current and open-circuit voltage, are introduced. An algorithm to compute the photoconversion efficiency of HIT elements taking into account the peculiarities of the open-circuit voltage generation, in particular, its rather high values, is proposed. To test the theoretical predictions against the experimental results, HIT elements with the efficiency of about 20 % are manufactured, and their short-circuit current, open-circuit voltage, photoconversion power, and fill factor of the current-voltage curve are measured as a function of temperature in a wide temperature range from 80 to 420 K. At low temperatures, the open-circuit voltage and the photoconversion power decrease as temperature is reduced. At T ≥ 200 K, the theoretical expressions and the experimental curves agree rather well. The behavior of the fill factor and output power at low temperatures is explained by the increase of the series resistance on cooling. The reasons behind the reduction of the power temperature coefficient in HIT elements are discussed and shown to be related to the low surface and volume recombination rates. Finally, a theoretical expression for the HIT element's temperature under natural working conditions is derived.