In this article, the wire electrical discharge machining of different heights of die steel workpieces has been carried out for different control strategies, i.e. proportional control mode, constant speed mode, constant voltage mode, and constant area feeding mode. It is very crucial to understand the thermo-mechanical aspect of the machining gap during machining of changing job height. For the efficient machining of variable thickness of jobs, these observations are extremely essential. Here, it is observed how job height influences cutting speed, surface roughness, kerf width, gap voltage, gap current, input power, and specific energy consumption under these control strategies. So far, very little research work has been reported in this area. Thus, it is quite imperative to carry out an intensive research study of wire electrical discharge machining (WEDM) during machining of different job thickness under those control strategies. An attempt has been made to understand the nature of variation of these important response parameters. The average and variance of some of the most influential parameters, i.e., cutting speed, surface finish, and kerf width were also calculated. Along with this, to predict the different important response parameters, i.e., cutting speed, surface finish, and kerf width for any given height job under any specified control strategy, regression analysis was carried out.