The current ramp up phase of ITER demonstration discharges, performed at JET, is analysed and the capability of the empirical L-mode Bohm-gyroBohm and Coppi-Tang transport models as well as the theory-based GLF23 model to predict the temperature evolution in these discharges is examined. The analysed database includes OHmic (OH) plasmas with various current ramp rates and plasma densities and the L-mode plasmas with the Ion Cyclotron Radio Frequency (ICRF) and Neutral Beam Injection (NBI) heating performed at various ICRF resonance positions and NBI heating powers. The emphasis of this analysis is a data consistency test, which is particularly important here because some parameters, useful for the transport model validation, are not measured in OH and ICRF heated plasmas (e.g. ion temperature, effective charge). The sensitivity of the predictive accuracy of the transport models to the unmeasured data is estimated. It is found that the Bohm-gyroBohm model satisfactorily predicts the temperature evolution in discharges with central heating (the rms deviation between the simulated and measured temperature is within 15%), but underestimates the thermal electron transport in the OH and off-axis ICRF heated discharges. The Coppi-Tang model strongly underestimates the thermal transport in all discharges considered. A re-normalisation of these empirical models for improving their predictive capability is proposed. The GLF23 model, strongly dependent on the ion temperature gradient and tested only for NBI heated discharges with measured ion temperatures, predicts accurately the temperature in the low power NBI heated discharge (rms < 10%) while the discrepancy with the data increases at high power. Based on the analysis of the JET discharges, the modelling of the current ramp up phase for the H-mode ITER scenario is performed with particular emphasis on the sensitivity of the duration of the sawtooth-free current ramp up phase to transport model.