We studied the nonlinear optical properties of single layer graphene using high terahertz (THz) fields. With the use of a back gate and cooling down the sample to cryogenic temperatures we are able to spectrally probe the nonlinear THz properties of intrinsic to highly doped graphene. The carrier density strongly affects the nonlinear properties of graphene; in the low doping and high THz field regime, an increase of the transmission on the order of 4% is found in our experiments. At higher doping levels we observe a larger relative nonlinear response: the larger the doping in the single layer the larger the relative field induced increase in transmission becomes. In all experiments, the THz field is opposing the effect of the gate, but field effects are never larger than the doping effects. We use the thermodynamical model for a hot electron gas also used by Mics et al (2015 Nat. Commun.. 6 7655) to simulate our data and study the effects of doping on the nonlinear properties of single layer graphene. We find that the highest carrier temperatures are obtained in low doped graphene. The model shows a good qualitative agreement with our data for high doping levels. Nevertheless our results demonstrate the limitation of the model for low doping levels. Our results are a road map for further explorations for the control of nonlinear light-matter interaction and functionalization of graphene layers in active THz devices in which carrier temperature and saturable absorption play a role.