Studies of binary evolution have, until recently, neglected thermal timescale mass transfer (TTMT). Recent work has suggested that this previously poorly studied area is crucial in the understanding of systems across the compact binary spectrum. We use the state-of-the-art binary population synthesis code BiSEPS (Willems and Kolb, 2002, MNRAS 337 1004-1016). However, the present treatment of TTMT is incomplete due to the nonlinear behaviour of stars in their departure from gravothermal ‘equilibrium’. Here we show work that should update the ultrafast stellar evolution algorithms within BiSEPS to make it the first pseudo-analytic code that can follow TTMT properly. We have generated fits to a set of over 300 Case B TTMT sequences with a range of intermediate-mass donors. These fits produce very good first approximations to both HR diagrams and mass-transfer rates (see figures 1 and 2), which we later hope to improve and extend. They are already a significant improvement over the previous fits.