This paper presents a mathematical model that could assist in measuring, monitoring and controlling temperature variation in cold and ‘red-hot’ metal working conditions of machining. A numerical analysis technique of the temperature distribution, based on the theory of complex applied potential, was carried out using the principles of relationship analysis between the paths of heat supply in Cartesian plane when the heat path supplied to the material is orthogonal. The high level of temperature involved may effectively be predicted if a mathematical relationship that predicts the pattern of temperature distribution in a material is available. A case study example in a machining workshop is given. Simulation experiments are then carried out using Monte Carlo to increase the confidence in decision-making and provide data for significance testing. This was used as an input for testing for significance. Sensitivity analyses were also carried out in order to observe the degree of responsiveness of model parameters to changes in value. In all, five pairs of comparison were carried out among different workpiece materials. There are significant differences between workpiece materials made of steel and copper, copper and zinc, copper and aluminum. However, no significant differences exist in the model behavior of steel and aluminum, steel and zinc. It was observed that parameters are highly sensitive to changes in value. The framework could possibly be applied to milling and surfacing activities in the engineering workshop. This contribution may be helpful to small-scale enterprises that could not afford sophisticated and very expensive facilities.