Hi,
Constant current source:
I think there is no need for it.
The supply voltage is constant and the LED forward voltage is constant and the resustor us constant (all within their drifts).
Therefore the current is constant, too.
V_BE of Q2 sets the current (in combination with the current sensing resistor). It is around 560mV and drift with about -2mV/°C.
--> A temperature change of 10°C leads to 20mV drift this is 3.6%.
I assume this drift is no benefit compared to the "single resistor" solution.
The given circuit makes sense when you don't have a regulated supply voltage... like the battery alone...
****
but the changes are in milivolts
You still don't give any information about what you want to achieve with your circuit.
I don't know where in the circuit those "millivolts" are...and you don't give any specifications.
Therefore it's impossible to help.
Klaus