This work is devoted to an experimental study of the thermal stability of a multichannel timing system with picosecond precession. The main area of application of the observed multichannel synchronization system is satellite laser ranging (SLR) stations with several pulsed radiation sources. The possibilities of multichannel measurements will significantly increase the accuracy of measurements and open up new opportunities for scientists working in satellite positioning, synchronization, geodesy, etc. The concept of the developed multichannel system, including the proposed synchronisation method, is described. The prototype consists of five independent event timers, an AFG (arbitrary function generator), a reference clock active splitter, and a controllable equal delay multiplexer. The AFG generates a 10 MHz reference clock and an event signal (1 PPS). All five event timers and a controlled delay multiplexer are connected to the PC from which they are controlled. The thermal chamber was used to organize measurements of thermal stability. The temperature in the thermal chamber was changed from 15 to 30°C, and the initial calibration of the system was carried out at a temperature of 22.5°C.