The temperature difference in the working range of precision instruments is large, and the change in temperature causes the static friction coefficient between the internal assembly contact surfaces to change. The change of the static friction coefficient will cause asymmetric displacement of the contact surface, which will affect the accuracy and stability of the instrument during operation. In order to study the non-linear variation law of the static friction coefficient under different temperature conditions, this paper proposes a method to measure the static friction coefficient at different temperatures accurately and designs and develops the corresponding static friction coefficient measuring device. The static friction coefficient of a typical steel-steel contact surface was measured from 20°C to 80°C using the static friction coefficient measuring device. It was found to be non-linear with increasing temperature, with the average static friction coefficient changing by about 5% at a temperature difference of 60°C. Based on the experimental data, a simulation study on the effect of non-linear variation of static friction coefficient at different temperatures was conducted using a simulated sample of a gyroscope assembly structure, and it was found that the asymmetric deformation of the assembly structure caused by the variation of static friction coefficient will be one of the factors causing the change of gyroscope accuracy stability. This research has important implications for maintaining and optimizing precision instrumentation accuracy stability.