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The increasing share of renewable energy sources in energy systems will lead to unpredictable moments of surplus/deficit in energy production. To address this issue, users with heat pumps can provide support to power grid operators through flexible unit operation achieved via Demand Response programs. For buildings connected to low-temperature heating networks with ensured third-party access, further room for flexibility can be explored by investigating the production of surplus heat that can be sold to the network. A key aspect lies in the identification of the energy pricing options that could encourage such flexible operation of a heat pump by “thermal prosumers”. To this aim, the present study investigates the impact of ad hoc variations in the electricity purchasing price through discounts or penalties included in the “network cost” component of the price on cost-effective operation of a heat pump connected to the thermal network. To discuss the effects of different pricing options in terms of increased flexibility, an office building located in Italy and equipped with a high-temperature heat pump is adopted as the case study. A heuristic profit-oriented management strategy of the heat pump is assumed, and dynamic simulations are performed. The results indicate that at current electricity prices, the heat pump operation is profitable both when supplying the heat to meet the building’s requirements and when producing surplus heat for sale to the thermal network. In addition, it is revealed that the penalties applied to the electricity purchasing price are effective in encouraging changes in the heat pump operation strategy, reducing its average production (the building increasingly relying on buying heat from the network) and the associated electricity consumption by 46.0% and 79.7% in the “light” and “severe” local power deficit scenarios, respectively.