Interaction of intense terahertz (THz) waves with graphene based modulation devices holds great potential for the opto-electronic applications of the future. Here we present a thin film graphene based THz perfect absorbing device, whose absorption and phase characteristics can be modulated through THz self-actions in the sub-ps time scale. The device consists of a single layer graphene placed on an ionic liquid substrate, back-plated by a metallic back-reflector, with the graphene doping level mediated through electrostatic gating. We experimentally record an absorption modulation of more than three orders of magnitude from the initial perfect absorption state, when the device is illuminated with THz field strengths in the range of 102 kV/cm to 654 kV/cm. Furthermore, an absolute phase modulation of 130°is recorded. Detailed theoretical analysis indicates that the origin of the THz nonlinear response is the THz induced heating of the graphene's carriers, that leads to a reduction of its conductivity, and consequently to reduced absorption of the THz radiation. Our analysis also maps the temporal dynamics of the THz induced temperature elevation of the graphene carriers, illustrating the ultrafast, sub-ps nature of the overall process. These results can find applications in future dynamically controlled flat optics and spatiotemporal shaping of intense THz electric fields.