The decarbonization of buildings requires the phase-out of fossil fuel heating systems. Heat pumps are considered a crucial technology to supply a substantial part of heating energy for buildings. Yet, their introduction is not without challenges, as heat pumps generate additional electricity demand as well as peak loads. To better understand these challenges, an ambitious simultaneous heat pump rollout in several central European countries with an hourly-resolved capacity expansion model of the power sector is studied. I assess the structure of hours and periods of peak heat demands and their concurrence with hours and periods of peak residual load. In a 2030 scenario, I find that meeting 25% of total heat demand in buildings with heat pumps would be covered best with additional wind power generation capacities. I also identify the important role of small thermal energy storage that could reduce the need for additional firm generation capacity. Due to the co-occurrence of heat demand, interconnection between countries does not substantially reduce the additional generation capacities needed for heat pump deployment. Based on six different weather years, my analysis cautions against relying on results based on a single weather year.