Focus on just the following part:Would you mind explaining how this circuit temperature change is very little? I don't get it. I also don't get how this circuit work

Assume that the circuit is stable at some temperature. The Vbe of Q2 will be at some particular voltage that is consistent with this stable operation. Without the diode, that voltage is the voltage drop across R6, which is sized to provide that voltage at the desired current.
Now consider what happens if the temperature rises. Due to the temperature coefficient of the transistor, the Vbe drops at the same collector current or, equivalently, at the same Vbe, the collector current increases. This results in more of the current in R2 being shunted away from the bases of Q6 and Q7, which results in a drop in LED current and a corresponding drop in the voltage across R6. Things will stabilize at a new, lower current at the higher temperature.
Another way to look at this is that, in order to hold the LED current at the same value, the Vbe voltage on Q2 must go down. But, with it connected directly to R6, the only way for that to happen is for the LED current to go down, which means that the LED can't hold the same current and will go down with temperature.
But what if we put another temperature-sensitive device between R6 and Q2 such that as the needed Vbe of Q2 drops, so does the voltage across this other device. If the two changes are equal, then the same voltage across R6 (i.e., the same LED current) will result in a Vbe across the transistor that is just the right amount lower to compensate for the lowering Vbe of Q2 at the desired operating point. The Vf of a Schottky diode has a temperature coefficient that is very close to that of the Vbe of an NON transistor. It's not a perfect match -- plus, R6 also has its own temperature coefficient (which is probably not reflected in the simulation model, but I don't know that for sure). So there will still be some residual effect of temperature change on LED current.




