Concentrations of water vapour entering the tropical lower stratosphere are primarily determined by conditions that air parcels encounter as they are transported through the tropical tropopause layer (TTL). Here we quantify the relative roles of variations in TTL temperatures and transport in determining seasonal and interannual variations of stratospheric water vapour. Following previous studies, we use trajectory calculations with the water vapour concentration set by the Lagrangian dry point (LDP) along trajectories. To assess the separate roles of transport and temperatures, the LDP calculations are modified by replacing either the winds or the temperatures with those from different years to investigate the wind or temperature sensitivity of water vapour to interannual variations and, correspondingly, with those from different months to investigate the wind or temperature sensitivity to seasonal variations. Both ERA-Interim reanalysis data for the 1999-2009 period and data generated by a chemistry-climate model (UM-UKCA) are investigated. Variations in temperatures, rather than transport, dominate interannual variability, typically explaining more than 70 % of variability, including individual events such as the 2000 stratospheric water vapour drop. Similarly seasonal variation of temperatures, rather than transport, is shown to be the dominant driver of the annual cycle in lower stratospheric water vapour concentrations in both the model and reanalysis, but it is also shown that seasonal variation of transport plays an important role in reducing the seasonal cycle maximum (reducing the annual range by about 30 %). The quantitative role in dehydration of sub-seasonal and sub-monthly Eulerian temperature variability is also examined by using time-filtered temperature fields in the trajectory calculations. Sub-monthly temperature variability reduces annual mean water vapour concentrations by 40 % in the reanalysis calculation and 30 % in the model calculation. As with other aspects of dehydration, simple Eulerian measures of variability are not sufficient to quantify the implications for dehydration, and the Lagrangian sampling of the variability must be taken into account. These results indicate that, whilst capturing seasonal and interannual variation of temperature is a major factor in modelling realistic stratospheric water vapour concentrations, simulation of seasonal variation of transport and of sub-seasonal and sub-monthly temperature variability are also important and cannot be ignored.