Abstract: Silicon photomultiplier (SiPM) is a new type of photoelectric conversion device with high gain and low power consumption since the 21st century. It consists of thousands of single photon avalanche diodes (SPADs) operating in Geiger mode connected in parallel with each other. It is widely used in medical imaging, high-energy physics, environmental monitoring and defence and security. The SiPM coupled with cerium-doped gadolinium gallium aluminium garnet (GAGG(Ce)) crystals is a promising detector for energy spectrum measurement and imaging detection. In this paper, the temperature drift characteristics of an 8×8 array SiPM-coupled Φ2 in×2 in GAGG(Ce) crystal detector were investigated, and a gain compensation system based on the feedback adjustment of the operating voltage of the SiPM-GAGG(Ce) detector by a temperature sensor was designed and built. Experiments such as power supply reliability test, power supply ripple test and temperature compensation test were carried out separately. The experimental results show that the power supply has high long-term operating stability and the power supply ripple noise is less than 0.001%. The output voltage range is 0-100 V, meeting the operating voltage requirements of most common SiPM models. The experimental results show that in the temperature range of -20-40 ℃. The maximum peak sites of 662, 1 173, 1 332, and 59.5 keV full-energy peaks are 515.9, 915.8, 1 041.0, and 43.1, and the minimum peak sites are 507.1, 899.0, 1 022.9, and 43.1. The maximum positive drifts are 4.6, 7.8, 8.1 and 0.5 lanes and the maximum negative drifts are 4.2, 8.7, 9.8 and 0.5 lanes respectively. Compared to the 662 keV for ¹³⁷Cs, 1 173 and 1 332 keV for ⁶⁰Co and 59.5 keV for ²⁴¹Am peak sites measured without temperature compensation, the average drifts of the peak sites with SiPM-only temperature compensation are reduced from 45.34%, 45.13%, 44.98%, and 43.85% to 23.68%, 23.67%, 23.68% and 18.30%. The temperature effect of the scintillation crystal has to be taken into account for the temperature compensation of the whole detector. After the overall temperature compensation of the SiPM-GAGG(Ce) detector, the average drift rates of 662 keV for ¹³⁷Cs, 1 173 keV and 1 332 keV for ⁶⁰Co and 59.5 keV for ²⁴¹Am peak channel sites are reduced to 0.37%, 0.37%, 0.36% and 0.57%, which is a significant compensation effect. In the absence of temperature compensation, the ¹³⁷Cs energy resolution varies from 8.08% at -20 ℃ to 14.58% at 40 ℃. After compensating for the temperature effect of the SiPM-GAGG(Ce) detector, the137Cs energy resolution changes from 8.36% at -20 ℃ to 9.29% at 40 ℃. The stability of the energy resolution is significantly improved. The temperature compensation system has the advantages of low noise, small size and freely customisable temperature characteristic curves. It effectively solves the problem of significant differences in the driving voltage of SiPM from different manufacturers and the compensation of temperature effects after coupling the 8×8 SiPM array with Φ2 in×2 in GAGG(Ce) crystals, and significantly improves the stability of the γ spectrometry system.