Today, the control of heat pumps aims to first and foremost maintain a comfortable indoor temperature. This is primarily done by deciding input power based on outside temperature. The cost of electricity, which can be rather volatile, is not taken into account. Electricity price can be provided on an hourly rate, and since a house can store thermal energy for a duration of time, it is possible to move electricity consumption to hours when electricity is cheap. In this thesis, the strategy used in the developed controller is Model Predictive Control (MPC). It is a suitable strategy because of the ability to incorporate an objective function that can be designed to take the trade-off between indoor temperature and electricity cost into account. The MPC prediction horizon is dynamic as the horizon of known electricity spot prices varies between 12 and 36 hours throughout the day. We model a residential house heated with a ground source heat pump for use in a case analysis. Sampled weather and spot price data for three different weeks are used in computer simulations. The developed MPC controller is compared with a classic \textit{heat curve} controller, as well as with variations of the MPC controller to estimate the effects of prediction and model errors.  The MPC controller is found to be able to reduce the electricity cost and/or provide better comfort and the prioritization of these factors can be changed depending on user preferences. When shifting energy consumption in time it is necessary to store thermal energy somewhere. If the house itself is used for this purpose, variations in indoor temperature must be accepted. Further, accurate modeling of the Coefficient of Performance (COP) is essential for ground source heat pumps. The COP varies significantly depending on operating conditions and the MPC controller must therefore have a correct perception of the COP. Publicly available weather forecasts are of sufficient quality to be usable for future prediction of outside temperature. For future studies, it would be advantageous if better models can be developed for prediction of global radiation. Including radiation in the MPC controller model would enable better comfort with very similar operating costs compared to when the MPC controller does not take radiation into account.