We present a new method for calculating the temperature profile in high explosive (HE) material using a Convolutional Neural Network (CNN). To train/test the CNN, we have developed a hybrid experiment/simulation method for collecting acoustic and temperature data. We experimentally heat cylindrical containers of HE material until detonation/deflagration, where we continuously measure the acoustic bursts through the HE using multiple acoustic transducers lined around the exterior container circumference. However, measuring the temperature profile in the HE in experiment would require inserting a high number of thermal probes, which would disrupt the heating process. Thus, we use two thermal probes, one at the HE center and one at the wall. We then use finite element simulation of the heating process to calculate the temperature distribution, and correct the simulated temperatures based on the experimental center and wall temperatures. We calculate temperature errors on the order of 15{\deg}C, which is approximately 12% of the range of temperatures in the experiment. We also investigate how the algorithm accuracy is affected by the number of acoustic receivers used to collect each measurement and the resolution of the temperature prediction. This work provides a means of assessing the safety status of HE material, which cannot be achieved using existing temperature measurement methods. Additionally, it has implications for range of other applications where internal temperature profile measurements would provide critical information. These applications include detecting chemical reactions, observing thermodynamic processes like combustion, monitoring metal or plastic casting, determining the energy density in thermal storage capsules, and identifying abnormal battery operation.