Multiprincipally designed concentrated solid solution alloys, such as high entropy alloys (HEA) and equiatomic multi-component alloys (EAMC-alloys) have shown much promise for use as structural components in future nuclear energy production concepts. The irradiation tolerance in these novel alloys has been shown to be superior to that in more conventional metals used in current nuclear reactors. However, studies involving irradiation of HEAs and EAMC-alloys have usually been performed at room temperature. Hence, in this study the irradiation damage is investigated computationally in two different Ni-based EAMC-alloys and pure Ni at four different temperatures, ranging from 138 K to 800 K. The irradiation damage was studied by analyzing point defects, defect cluster sizes and dislocation networks in the materials. Dislocation loop mobility calculations were performed to help understanding the formation of different dislocation networks in the irradiated materials. Utilizing the knowledge of the depth distribution of damage, and using simulations of Rutherford backscattering in channeling conditions (RBS/c), we can relate our results to experimental data. The main findings are that the alloys have superior irradiation tolerance at all temperatures as compared to pure Ni, and that the damage is reduced in all materials with an increase in temperature.