The power dissipation is not a big issue, imho, as it will be constant. We talk here the feedback divider - the biggest trouble maker with the 7->10V amplifier.
With say (R1+R2) in a typical range 5k to 20k the Ptot will be 20mW to 5mW. That is not small, but constant (as the 10V output will be +/- couple of ppm worst case).
With both R1 and R2 wound on the same bobbin the temperature difference between R1 and R2 should stay constant, afaik. With changing the ambient the temperature of (R1+R2) will change accordingly, but the difference stays the same.
The ratio will be
Ratio = R1*(1+TC*(Tr1-25)) / R2*(1+TC(Tr2-25)), where (Tr1+Tamb)-(Tr2+Tamb)=const.
Basically the Vishay divider with 3 legs
![Tongue :P](https://www.eevblog.com/forum/Smileys/default/xtongue.gif.pagespeed.ic.J5mTe0A2NA.png)
PS: I would even try with lower valued (R1+R2), like 1k. We use usually transistor buffer at the output, thus the 10mA via the divider cannot hurt (100mW), imho, the elevated temperature of the divider may even help to repel the humidity inside the resistor off.