The increase of power plants' conversion efficiencies, together with the high share of renewable energy sources in the electricity production for some countries, pushes for the use of heat pumps for space heating when aiming at reducing the associated primary energy consumption. However, the effective reduction of primary energy consumption should be supported by careful evaluations, as a number of parameters influence the heat pumps performance, including outdoor temperature, supply temperature, heat load and electricity primary energy factor. The variability of such parameters increases the complexity of the analysis, and annual or monthly average calculations might lead to incomplete evaluations and thus to sub-optimal solutions. This paper performs a hourly simulation of the operation of an air-source heat pump for space heating, relying on the available heat demand data of real buildings currently connected to a district heating network. In addition, the paper proposes the calculation of the hourly primary energy factor of the electricity supplied by the power grid, as the variability of the generation sources plays a key role in the global analysis of the energy system's conversion efficiency. The results show that in all the considered cases the heat pumps provide potential primary energy savings compared to natural gas boilers, thanks to the combined effect of their high coefficient of performance and the low electricity primary energy factor in the analyzed context. The primary energy consumption reduction obtained in each case is in the range 10-40%, with a median value close to 30%. Moreover, the comparison between average and high-resolution calculations of primary energy factors shows the possible underestimation of the potential primary energy savings when yearly or monthly data are adopted.