This paper analyzes slip on a fluid-infiltrated dilatant fault for imposed (tectonic) strain rates much slower than the rate of fluid exchange between the gouge zone and the surroundings and for exchange of heat slower than of fluid, typical of interseismic or most laboratory loading conditions. The limiting solution, corresponding to the infinitely rapid drainage rate, developed in the companion paper by Garagash and Rudnicki <2003>, yielded unbounded slip acceleration for sufficiently large slip weakening of the fault. Analysis for rapid but finite drainage rates (quasi-drained condition) reveals two types of possible instability. The first is inertial instability (a seismic event) characterized by an unbounded slip rate and attributed to the destabilizing effects of shear heating and fault slip weakening. The second corresponds to loss of uniqueness and arises from the small pressure increase caused by shear heating for rapid but finite rates of drainage. This instability emerges for even small amounts of thermomechanical coupling and a large range of dilatancy and slip weakening. Its resolution probably requires a more elaborate frictional description (e.g., rate and state), but within the slip-weakening framework here, leads to either slip arrest or inertial instability. The response is always unstable (in one of these two ways) for sufficiently large thermal coupling or initial stress regardless of the amount of slip weakening and dilatancy. The counterintuitive stabilizing effect of increased slip weakening or decreased dilatancy, similar to the effect in the companion paper, also occurs for nearly drained slip.