Real-time prediction of product temperature is a challenge for cold chain monitoring. The use of machine learning methods, especially neural networks, has been suggested as a possible approach. However, their training requires a large amount of good quality data. We found that experimental data leads to better results (by 20 to 40% compared with synthetic data) but require material investment, while synthetic data generated from thermal model is plentiful but tends to cause overfitting and overestimation of prediction performance (up to 150%). Our study shows that increasing the amount of synthetic data only decreases the variance, but not the mean error. The best strategy is to improve the thermal model used. As for experimental data, it is more useful to find an optimal position of the sensor in the pallet than using ever increasing realistic scenarios. Overall, even with imperfect predictions, machine learning models are able to predict temperature in real time thus enabling to take preventive measures when needed.