Two preliminary design concepts for the low T-C. superconductor Toroidal Field coil system of the planned European fusion reactor DEMO were proposed in 2012 by EPFL-CRPP PSI Villigen and ENEA Frascati. The coil consists of eight double layers (DLs) wound using: a) flat multistage cables with two side cooling channels (CRPP design) or b) rectangular CICC with a central cooling channel (ENEA design). The present study is focused on the thermal-hydraulic analysis of the candidate conductor designs, namely: i) hydraulic analysis-calculation of the mass flow rates in each conductor at the expected value of pressure drop in the coil at operating conditions, ii) heat removal analysis-calculation of mass flow rates and the helium outlet temperatures in each conductor as functions of the heat deposition rate, iii) assessment of the hot spot temperature and the maximum pressure in each conductor during quench. The results of our analysis provide the information for further improvement and optimization of the conductors' design.