The present research compared the behaviours of lightweight mortars based on ordinary Portland cement (OPC), calcium sulphoaluminate cement (CSAC), and calcium aluminate cement (CAC) containing expanded perlite and subjected to elevated temperatures. The perlite substituted natural sand in amounts of 25, 50, 75, and 100% by volume. The mortars were subjected to heating at up to 300 °C, 650 °C, and 1000 °C at a rate of 20 °C/min. The consistency and density of fresh mortars, compressive strength and density of hardened mortars after heating and cooling, and absorbability were assessed. Such a holistic testing approach is the main novelty of this research, which is related to the aforementioned mixtures and elevated temperatures. The main contribution of this article is a comparison of various cement types coupled with variations in the level of sand replacement with expanded perlite. In previous studies, comparisons were made in pairs of OPC-CSAC and OPC-CAC for normal-weight concrete. There is a gap in our knowledge of triple comparisons and lightweight cement composites which is filled by the current study. The use of OPC at up to 650 °C is recommended because it is the most common solution, its performance is similar to that of CAC, and it is cheaper than other solutions. Above 650 °C and up to 1000 °C, CAC is the only solution because it performs better than other cements. CSAC is not suitable for use at elevated temperatures because of its poor strength performance, even if it is the best solution from an environmental point of view. Sand replacement with perlite does not increase the strength performance under elevated temperatures, but its efficiency is different for various types of cement.