In this work, a thermodynamic model was developed for a three-pass firetube boiler operating in a steady state with Bolivian natural gas. The sensitivity in the temperature profile of various heat exchange correlations found in the literature was tested. A central composite design made it possible to simultaneously evaluate the impact of the variation of six parameters (diameter of tubes in the first and two subsequent passes, boiler length, number of tubes in the second and third passes and percentage of excess air in combustion) and obtain an empirical polynomial model to optimize boiler energy and exergetic efficiencies. A mesh test was performed with temperatures at the end of the flame, combustion chamber, second and third passes and pointed to from 200 divisions in each pass the impact of volume is no longer significant on temperature. The model was validated with data obtained experimentally, observing that the difference between the experimental and theoretical values of the temperatures of the first and second passes is less than 22.9 degrees C and less than 43.9 degrees C in the third pass. With the robust polynomial models obtained with the design of experiments, it was possible to observe the most significant parameters, both for energy and exergetic efficiencies, as well as for exergy destruction. They are, in decreasing order of importance: excess air; the two contributions associated with the length of the caldera; the number of tubes in the second and third passes and the diameter of the tubes in the second and third pass and the diameter of the tube in the first pass. In addition, it was possible to quantify the trade-off between increasing the heat exchange surface and maintaining the flow turbulence level.