The main objective of applying Natural gas pressure reduction station or city gate stations (CGS) is to adjust gas pressure using heater for the home usages within a standard range. Since thermal efficiency and fuel consumption of these heaters have great importance, effect of six influential parameters namely length of gas-coil, diameter of gas-coil, radius of heater shell, length of heater shell, fire tube diameter and length on amount of fuel consumption and thermal efficiency are considered in this study using Sobol statistical sensitivity analysis. Results show that gas-coil length and diameter are not effective on fuel consumption and thermal efficiency. On the contrary, increasing heater shell radius, heater shell length and fire tube radius have the same effect so that they, individually, cause a linear increase in fuel consumption. According to results taken from Sobol analysis they similarly have the influence of 19-23% on fuel consumption and 21-22% on thermal efficiency. Finally, it was revealed that effect of fire tube length on fuel consumption and thermal efficiency of the heater was 37% and 35% respectively.