Efficient and compact long-term heat storage material would enable effective utilization of renewable energy sources by balancing the long-term variations in production and consumption. However, current materials still require higher storage capacity, efficiency and reliability for large-scale use. Previously, we established that cold-crystallizing material (CCM), which consists of erythritol in a polymer matrix, can reliably store heat over three months without decreasing its storage efficiency. Heat is stored by cooling the melted CCM to deeply supercooled state (storage temperature at 0-10 degrees C) and released by heating the material to cold-crystallization temperature, which initiates crystallization (i.e. coldcrystallization). However, if the storage temperature of CCM was increased, stored melting heat would dissipate due to slow crystallization. This paper analyses cold-crystallization rate of CCM, in order to model and predict the storage efficiency at different storage temperatures. This was carried out by measuring the progress of cold-crystallization by differential scanning calorimetry (DSC) under multiple isothermal conditions. The crystallization data was first analysed by applying Avrami approach, to identify the crystallization rate constant. Then, the Arrhenius and the Williams-Landel-Ferry (WLF) models estimated the temperature dependence of the rate constant. DSC measurements yielded a storage efficiency of around 0.74 in the tested temperature range. Time evolution of this storage efficiency predicted with the WLF model corresponds to the experimental data indicating that valid predictions of CCM's storage efficiency can be obtained, when storage temperature and time are known.