Given that surface roughness is used to determine product quality, it is a crucial consideration in turning machining. Moreover, it considerably affects the cost of machining. This study forecasts surface roughness values for AISI 304 stainless-steel hot lathe machining using the particle swarm optimisation (PSO) methodology. The workpiece is heated to 100, 150 or 200 degrees Celsius before being turned. Afterwards, the depth, speed and feeding rate of cutting are adjusted to determine the surface roughness of the workpiece. The feeding rate is determined to be the most considerable influence in raising the surface roughness value, followed by cutting depth, cutting speed and workpiece temperature. In terms of accuracy, empirical modelling performs better. The PSO methodology illustrates an effective and straightforward method that can be applied to calibrate different empirical machining models.