Q3's current _IS_ nominally independent of temperature. It consists of two components -- the IPTAT in Q1 (or Q2), and the I_VBE in R1 (or R2). R0, R1 & R2 are chosen to give a net 0TC in the output (except for the quadratic term you are trying to remove).

Another way of thinking about this is that the output V across R3 is 0TC, since M4==M3, the current in Q3 is constant.

This 'constant' does not include actual tempcos in the resistors -- generally R's have a +ve tempco -- say +1000ppm/°C. This will also turn up in the true current in Q3 etc. (but still is compensated in the output).

The curvature correction slightly modifies the current in Q3, but you won't see it unless you look very closely.

Generally, the curvature correction required also depends on the tempco of the R's -- this paper doesn't include that data. You may find that you need different amounts of correction than the straightforward theory predicts. Try and simulate with ideal resistors first.

If your diodes are poor, you will need additional changes, so it is best to allow some design headroom for not-well-modelled effects also.