The solid state photon counting detector is one of the key components of a measurement chain for laser time transfer ground to space. The photon counting approach significantly reduces systematic errors of the time transfer. The requirements put on the detection precision and the stability of laser time transfer are increasing and reaching sub-picosecond levels now. The temperature variations in the space environment limit the long term detection delay stability of detectors. Therefore, we have modified the existing space qualified solid state photon counter control circuit which compensates to a high degree the temperature variations of detection delay. We have optimized the detection delay change with operating temperature and reached the lowest temperature coefficient as low as 20 fs/K in a temperature range of +22 to +46 °C. The timing resolution and photon detection probability remained unchanged at the values of 40 ps FWHM and 30%, respectively. Thanks to the low temperature drift of the detector, the limiting precision of the laser time transfer chain characterized by time deviation is lower than 40 fs for 2000 s averaging time. These detection delay stability parameters are, to our knowledge, the best ever reported for any photon counting detector. This modification of the detector control circuit did not affect the space qualification of the device, which is expected to be used in future laser time transfer space missions.