This study has compared different methods to predict the simultaneous effects of conductive and radiative heat transfer in a polymethylmethacrylate (PMMA) sample. PMMA is a type of polymer utilized in various sensors and actuator devices. One-dimensional combined heat transfer is considered in numerical analysis. Computer implementation was obtained for the numerical solution of the governing equation with the implicit finite difference method in the case of discretization. Kirchhoff transformation was used to obtain data from a non-linear equation of conductive heat transfer by considering monochromatic radiation intensity and temperature conditions applied to the PMMA sample boundaries. For the deep neural network (DNN) method, the novel long short-term memory (LSTM) method was introduced to find accurate results in the least processing time compared to the numerical method. A recent study derived the combined heat transfer and temperature profiles for the PMMA sample. Furthermore, the transient temperature profile was validated by another study. A comparison proves the perfect agreement. It shows the temperature gradient in the primary positions, which provides a spectral amount of conductive heat transfer from the PMMA sample. It is more straightforward when they are compared with the novel DNN method. Results demonstrate that this artificial intelligence method is accurate and fast in predicting problems. By analyzing the results from the numerical solution, it can be understood that the conductive and radiative heat flux are similar in the case of gradient behavior, but the amount is also twice as high approximately. Hence, total heat flux has a constant value in an approximated steady-state condition. In addition to analyzing their composition, the receiver operating characteristic (ROC) curve and confusion matrix were implemented to evaluate the algorithm’s performance.