The transverse momentum distribution of the diffractive final state provides an interesting test of models of diffractive deep-inelastic scattering at HERA. We present a comparison of several colour-singlet exchange models with thrust transverse momentum data from a recent H1 analysis. We also study the effect of constraints imposed on the kinematically-accessible phase space by data selection cuts and find that, as a result of the pseudo-rapidity cut which is used by H1 to select diffractive events, there is no dijet contribution at low transverse momenta. We are able to fit the large transverse momentum part of the data with a two-gluon dijet model. The results of this analysis are compared with a previous study of large pseudo-rapidity gap structure function data, and we discuss ways in which one might reconcile the results of the two analyses. We conclude that a significant small-$\beta$ 3-jet contribution is probably required to explain the data, and show that the combination of a two-gluon dijet model and an exponentially-decaying thrust transverse momentum distribution provides a good fit over the entire kinematic range of the thrust data.