The dramatic effects of viscous dissipation on the stability of Newtonian Taylor–Couette (TC) flows are studied experimentally using flow visualization techniques. Viscous heating, parameterized by the Nahme–Griffith number Na, drives a transition to a new, oscillatory mode of instability when coupled with the effects of centrifugal destabilization. This instability, consisting of travelling axisymmetric vortices, only occurs when viscous heating and centrifugal destabilization are both present. Step tests in cylinder velocity show that the time following initiation of shearing required for onset of instability scales well with the time for the fluid to reach a steady temperature profile under the action of viscous heating. The onset time can be dramatically reduced at fixed Na by increasing the centrifugal destabilization through the addition of co-rotation of the outer cylinder. The onset time can also be reduced while holding the centrifugal destabilization constant by increasing the amount of viscous heating (i.e. holding Reynolds number Re constant while increasing Na). The effects of viscous heating on the critical conditions of Newtonian TC flows are also quantified using ramp tests in cylinder velocity. These tests reveal the large extent to which viscous heating is destabilizing; at Na ≈ 2, a transition occurs at a critical Re that is less than 5% of the isothermal value.