The performance of a magnetocaloric heat pump (MCHP) consisting of active magnetocaloric regenerators (AMR) of 12 layers of MnFePSi magnetocaloric materials (MCM) with a linear distribution of Curie temperatures was investigated using a 1D numerical model. The model predicted the heating power and coefficient of performance (COP) of the AMR for a fixed temperature span of 27 K, between 281 K and 308 K, and variable flow rate and AMR cycle frequency. A maximum applied magnetic field strength of 1.4 T was used. A well-insulated house with a maximum heating power demand of 3 kW (under quasi steady state conditions) was considered. Ambient temperature in The Netherlands was taken as a reference for the estimation of the seasonal heating power demand. Without optimizing the design of the AMR, the model predicts a maximum single-AMR heating power equal to 43.5 W when the AMR operates at 3 Hz and 3 L min^-1, and a maximum COP equal to 5.8 when it operates at 1.5 Hz and 1 L min^-1 Considering the maximum heating power of a single AMR, approximately 69 AMRs are needed to provide the design heating power demand of the house. It was found that it is possible to achieve an AMR seasonal COP of 5.6 by continuously adjusting the flow rate and frequency of operation of the MCHP along with the ON/OFF switching of some groups of AMRs in order to adjust the heating power of the MCHP to the heating power demand of the house.