The circuit above is used to detect an event at a certain input voltage. Nevertheless according to the temperature, the event is not detected at the same temperature as the VBE(ON) changes with the temperature.
Does anyone know how to compensate this circuit against temperature change ?
The simplest approximate way to compensate a transistor VBE is to place another diode, or better still a diode connected 2N2222, in series with R1. Unfortunately, that also cancels the 'reference' element of VBE that you are using.
Instead, consider using a TL431 or TLV431, using its adj terminal as the 'base', and it will behave like an NPN transistor, with a temperature stable 'VBE' of 1.25 V for the TLV431, or 2.5 V for the TL431.
The classic way is to use a temperature stable reference voltage into one terminal of a comparator.
You are using the Vbe as a reference, so cancelling it out won't do you much good.
An IC comparator with a reference, either divided from the power supply if that's good enough for you, or an IC reference, is one good solution.
Here's a simple discrete circuit that improves the temperature sensitivity by about 6:1 by adding a differential pair and using the power supply voltage as a reference:
