To find the temperature at stages 3 and 4 of a Diesel engine cycle, the formula for T3 is T3 = T2 + (Q1 / (m * cp), where Q1 is the heat input, T2 is the temperature at stage 2, m is mass, and cp is the specific heat at constant pressure. For T4, the formula is T4 = T3 * (V3/V4) ^ (k-1), requiring the volumes at stages 3 and 4 and the adiabatic constant k. Accurate calculations depend on knowing these variables, particularly the compression ratios and heat input. The discussion emphasizes clarity in questions to accommodate diverse participants.