The specific heat capacity of a material is of importance for thermal storage. Transient Plane Source (TPS) is a measurement method with a sensor that works both as a heat source and as a resistance thermometer. The standard TPS measurement gives the thermal conductivity and thermal diffusivity of an isotropic material which can be used to calculate the heat capacity. The thermal properties of an anisotropic material can be measured if the heat capacity is known. A method for heat capacity measurement exists, where the TPS sensor is attached to a golden sample container which is surrounded by insulation. However, its results are based on an assumption of negligible heat losses which leads to uncertainties in the results. From that position, this paper aims to give an answer of how to model the heat losses from the specific heat measurements with TPS. A new set-up is introduced, where the sensor with the container hangs freely in a steel tube in order to get more predictable heat losses. The results show that the measurements can be modelled as a network of lumps connected by conductances which can be approximated as constant. Thereby, the conductances out from the system can be solved from a reference measurement and used as input data for a model of a measurement with a sample. The model seems to underestimate the heat capacity, which might be a consequence of temperature dependent effects on the conductances from convection. The tube in the set-up could be evacuated to minimize those losses.