I don't think so. G/T is a measure in dB, the correct calculation is G/T(dB/k) = 10*log10(gain)-10*log10(T(Kelvin)).
For instance, if you have no gain and the noise temperature of your receptor is 299K
G/T (dB/K)= 10*log10(1) - 10*log10(299K) = 0 - 10*log10(299K) = -24.757 dB/K