The grinding process is a common choice for finishing of mechanical parts in industrial practice where both surface quality and integrity are required to be maintained at sufficiently high levels. As it is not always possible to obtain all the necessary information for process monitoring through experimental measurements, it is often necessary to develop numerical models, which can be validated based on experimental data and then used to predict various outcomes of the grinding process such as the temperature or the stress field in the workpiece. Nevertheless, when specific responses are required to be predicted in real time, numerical models cannot be directly used due to their computational cost and thus, machine learning methods can be employed as an alternative choice. In order to determine a method which can achieve both the required level of accuracy and reduced computational cost, two different models, namely NARX (nonlinear autoregressive exogenous model) and LSTM (long-short term memory), are compared for a case of peripheral grinding of steel components under different process conditions. Both machine learning models are trained based on data from a validated numerical model, and their accuracy regarding the prediction of temperature field in every case is evaluated through various criteria.