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We use simulations to examine current saturation in sub-micron graphene transistors on SiO2/Si. We find that self-heating is partly responsible for current saturation (lower output conductance) but degrades current densities above 1 bmA/μm by up to 15%. Heating effects are reduced if the supporting insulator is thinned or, in shorter channel devices, by partial heat sinking at the contacts. The transient behavior of such devices has thermal time constants of ~ 30-300 ns, which is dominated by the thickness of the supporting insulator and that of the device capping layers (a behavior also expected in ultrathin-body SOI transistors). The results shed important physical insight into the high-field and transient behavior of graphene transistors.