I solved the ideal gas law for T: T = PV/nR. Therefore, T', which is the rate of change of the temperature with respect to time is: ((PV)'(nR) - (PV)(nR)') / (nR)^2, by way of the product rule.
T' = ((PV)'(nR) - (PV)(nR)') / (nR)^2
= ((P'V + PV')(nR) - (PV)(n'R + nR')) / (nR)^2
Since you've got P', V', n', and you know derivative of a constant, R, is 0, you can solve for T'. I got approximately -45 K/sec for T'. Good luck.