Combined heat pumps and solar collectors got a renewed interest on the heating system market worldwide. Connected to the heat pump evaporator, unglazed solar collectors can considerably increase their efficiency, but they also raise the coefficient of performance of the heat pump with higher average temperature levels at the evaporator. Simulation of these systems requires a collector model that can take into account operation at very low temperatures (below freezing) and under various weather conditions, particularly operation without solar irradiation. A solar collector mathematical model is developed and evaluated considering, the condensation/frost effect and rain heat gains or losses. Also wind speed and long wave irradiation on both sides of the collector are treated. Results show important heat gains for unglazed solar collectors without solar irradiation. Up to 50% of additional heat gain was found due to the condensation phenomenon and up to 40% due to frost under no solar irradiation. This work also points out the influence of the operating conditions on the collector's characteristics. Based on experiments carried out at a test facility, every heat flux on the absorber was separately evaluated so that this model can represent a valuable tool in optimising the design or the thermal efficiency of the collector. It also enables the prediction of the total energy yield for solar thermal collectors under extreme operating conditions. (C) 2015 Elsevier Ltd. All rights reserved.