  We obtain theoretical expressions for the photocurrent in the Heterojunction
solar cells with Intrinsic Thin layer (HIT cells). Our calculations take into
account tunneling of electrons and holes through wide-bandgap layers of
$\alpha$-Si:H or $\alpha$-SiC:H. We introduce 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. We propose 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. We test our theoretical
predictions against the experimental results. For this, we fabricate HIT
elements with the efficiency of about $20\,\%$. We measured the temperature
dependence of the short-circuit current, open-circuit voltage, photoconversion
power, and fill factor of the current-voltage curve of these elements in a wide
temperature range from 80 to 420\,K. In the low-temperature range, the
open-circuit voltage and the photoconversion power decrease on cooling. At $T
\ge 200$\,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.
We discuss the reasons behind the reduction of the power temperature
coefficient in HIT elements. We show that they are related to the low value of
the combined surface and volume recombination rate. Finally, we derive a
theoretical expression for the HIT element's operation temperature under
natural working conditions.
