I'm trying to get a dimensionless form of the following expression:
\begin{equation} \delta (T) = a_{\delta} \left(\frac{1}{T}\right)^{b_\delta} + c_\delta ~, \end{equation}
so that the numerical values of the parameters ($a_{\delta}, {b_\delta}, c_\delta$) are independent of the selected system of units for temperature ($K$, $^o C$, etc.) [see Barenblatt, "Scaling", Cambridge Texts in Applied Mathematics, 1st ed. (2003)].
In fact, if I include a reference temperature, $T_0$, the expression above tends to be more consistent, but the first parameter $a_\delta$ still depends on the numerical value of the coefficient $(T_0 / T)$. The resulting expression will be:
\begin{equation} \delta (T) = a_{\delta} \left(\frac{T_0}{T}\right)^{b_\delta} + c_\delta ~. \end{equation}
Is better to perform a substraction of temperatures, given that a substraction between two temperatures in Celsius and Kelvin have both the same result? i.e.:
\begin{equation} \delta (T) = a_{\delta} \left(\frac{T_0}{T-T_0}\right)^{b_\delta} + c_\delta ~. \end{equation}
Note that $\delta$ is dimensionless.