In the lab experiments, the compressive strength (CS) of cement mortar, three pre-setting water/binder (W/B) ratios, five substitution rates of burned joss paper ash (SR-BJPA), and three curing temperatures (T) were tested for the 45 samples. The results were recorded at 3, 7, 28, 56, 90, and 120 days after curing (#days) for each sample. The correlations between CS and each experimental factor (W/B ratio, SR-BJPA, T, and #days) and the effects of each factor or pair of factors on CS were determined using four univariate and six bivariate regression models. All the models were significant (i.e., the factors and the pairs of factors can be used to predict CS); however, each model had a different ability to fit the data and explain the data variance, making some models not that suitable. The effects on CS of substituting cement with different BJPA proportions and curing the mortar at different temperatures were mainly identified. A knowledge base for predicting the CS was established before any sample is to be made in future practise. Finally, using an SR-BJPA of 5% and raising the curing temperature to 50 °C (or 75 °C, if additional heating energy consumption needs not be considered) while keeping the W/B ratio at 0.4 is recommended to obtain an optimal CS for the full-aged sample (i.e., at #days = 120) in future practise, subject to the aim to consume the BJPA wastes by using it to replace Portland cement, in order to reduce the vast volume of carbon emitted along with the production of the cement material.