Trains of auditory clicks increase subsequent judgements of stimulus duration by approximately 10%. Scalar timing theory suggests this is due to a 10% increase in pacemaker rate, a main component of the internal clock. The effect has been demonstrated in many timing tasks, including verbal estimation, temporal generalisation, and temporal bisection. However, the effect of click trains has yet to be examined on temporal sensitivity, commonly measured by temporal difference thresholds. We sought to investigate this both experimentally; where we found no significant increase in temporal sensitivity, and computationally; by modelling the temporal difference threshold task according to scalar timing theory. Our experimental null result presented three possibilities which we investigated by simulating a 10% increase in pacemaker rate in a newly-created scalar timing theory model of thresholds. We found that a 10% increase in pacemaker rate led to a significant improvement in temporal sensitivity in only 8.66% of 10,000 simulations. When a 74% increase in pacemaker rate was modelled to simulate the filled-duration illusion, temporal sensitivity was significantly improved in 55.36% of simulations. Therefore, scalar timing theory does predict improved temporal sensitivity for a faster pacemaker, but the effect of click trains (a supposed 10% increase) appears to be too small to be reliably found in the temporal difference threshold task.