With the growth of wind and solar energy in electricity supply, the electrification of space heating is becoming a promising decarbonization option. In turn, such electrification may help the power system integration of variable renewables, for two reasons: thermal storage could provide low-cost flexibility and heat demand is seasonally correlated with wind power. However, temporal fluctuations in heat demand may also imply new challenges for the power system. This study assesses the economic characteristics of electric heat pumps and wind energy and studies their interaction on wholesale electricity markets. Using a numerical electricity market model, we estimate the economic value of wind energy and the economic cost of powering heat pumps. We find that, just as expanding wind energy depresses its €/MWhel value, adopting heat pumps increases their €/MWhel cost. This rise can be mitigated by synergistic effects with wind power, "system-friendly" heat pump technology, and thermal storage. Furthermore, heat pumps raise the wind market value, but this effect vanishes if accounting for the additional wind energy needed to serve the heat pump load. Thermal storage facilitates the system integration of wind power but competes with other flexibility options. For an efficient adoption of heat pumps and thermal storage, we argued that retail tariffs for heat pump customers should reflect their underlying economic cost.