Viscous heating under high shear has been proposed as a possible cause for the accidental ignition of liquid monopropellants. A typical experiment consists of the rapid compression of a drop of liquid between two parallel solid plates. This process is simulated numerically by solving a boundary-layer version of the Navier-Stokes equations. It is found that allowing for the decrease of viscosity with increasing temperature leads to a major reduction in the estimated peak temperature. On the basis of these results, it would seem that accidental ignition by viscous heating is an unlikely event. The effect of wall slip is also briefly considered.