To operate the hydrogen sulphide gas coolers outside design parameters impacts the production process, because the resulting increased gas outlet temperature and lower sulphur separation effectiveness, which favors pipe plugging and damage to downstream compressors. A procedure was formulated for thermal analysis of jacketed shell-and-tube heat exchangers, in order to examine the object of study and propose improvements to existing facilities. Beyond conventional analysis, this work included the experimental method as well as mathematical modeling, that were not interrelated in previous researches. A cooling system that meets current technological requirements was identified, consisting of two sets of four improved coolers, where each set operates at a maximum hydrogen sulphide flowrate of 5.565 kg/s and 7.500 kg/s of water feeding each exchanger, thus reaching a gas cooling rate below 313 K.