Flexible controlled heat pumps in combination with thermal storages are expected to play a key role in near future energy systems exhibiting larger shares of renewable energies. In such systems, surplus energy from windfarms or PV will be stored and used later at times of higher energy demands and prices. For energy consumers, this will lead to cost savings while supporting the further expansion of renewable energies. In this work, these relevant cost savings are quantified using a linear programming approach. Furthermore, is this approach applied to different energy users, electricity tariffs and heat demands. As a result, it is shown that the potential variable cost savings with respect to heat users and electricity tariffs vary from 0.9 to 2.7 /MWh, and the potential load shift from 3 to 6 hours.