David,
Equations written in plain text are always hard to get a grip of. However, I guess the two equations you mentioned,
1/T = a + b(lnRt) + c(lnRt)^3
and
T = 1/ (a + lnRt*(b + c*(lnRt**2)))
are identical.
First invert the second eq. and multiply lnRt with c*(lnRt**2) in it. You will then get the first equation since
lnRt*c*(lnRt**2) = c(lnRt)^3.
I guess the confusion is that
lnRt**2 =(lnRt)^2 and not ln(Rt^2).
Hope this helps. /Mikael