To address the effect of temperature, we establish a temperature compensation model for gyroscope output signal using long short-term memory network (LSTM), support vector machine (SVM), and depth belief network (DBN). We develop a denoising algorithm using variational mode decomposition (VMD), and sampling entropy (SE) to eliminate the influence of factors other than temperature on the MEMS gyroscope. First, the signal is decomposed into several intrinsic mode functions (IMF) using VMD. Then, the decomposed IMFs are classified into three categories: feature terms, mixture terms, and noise terms using SE. These three categories of signals are processed separately, preserving the useful signal of the original signal while precisely removing the noise. Subsequently, the processed signals are reconstructed to obtain the reconstructed signals. Finally, we perform temperature experiments and find that the rate random wander and bias instability of the gyroscope compensated output signal are reduced by 84.35% and 95.57%, respectively.