MPU6050 shows a discontinuity when temperature varies

Hi,
I am using a MPU6050 to control an autopilot on my leisure boat. I only use the Z axis of the gyroscope.
In this special application, I need a very high sensitivity and moreover, a very high zero offset stability, for the used range for the rotational speed is only 2 deg/s. To keep in a straight line, I must stay within 1/100 deg/s.
I have observed large variations due to temperatures, and so far, I manually recalibrate the gyro periodically.
To improve this, I intend to put the gyro in a temperature-stabilized area. In this intent, I have plotted the gyro output against the temperature.
As expected, the variation of the output is large when the temperature varies; but what is strange, is that I observe discontinuities in the curves.
As you can see, after having heated the gyro then allowed it to cool down, during the cooling, a discontinuity is visible at about 32 Celsius. I repeated the experiment, and the phenomenon was reproduced the same way.
What could cause this strange behaviour? While it is allowable to have a temperature dependency, a discontinuity ruins any hope of stability!