I see, that is what I suspected, thank you.
If I tried to list all the relevant quantities in this problem I would get to something like:
T_i=T_i(u_{air}, T_{air},\rho_{air},c_{p,{air}},\nu_{air},\dot{m}_{coolant},\rho_{coolant},c_{p,{coolant}},\nu_{coolant},P_b(t),N(t),\beta(t)),
where the...