Recently a new semiconductor defect spectroscopy, namely positron deep level transient spectroscopy (PDLTS) has been proposed that combines the energy selectivity of deep level transient spectroscopy with the structural sensitivity of positron annihilation spectroscopy. This paper focuses on one variant of PDLTS, namely positron velocity PDLTS, which has no sensitivity towards vacancy defects but nevertheless is useful in studying deep levels in semi-insulators. In the present study the electric field within the depletion region of semi-insulting GaAs is monitored through the measurement of the small Doppler shift in the annihilation radiation that comes from this region as a result of positron drift. The drift is the result of an increasing electric field produced by space charge building up from ionizing deep level defects. Doppler shift transients are measured between 50-300K. The EL2 level emission transients are clearly seen at temperatures around 300K that yield E-C-0.78 +/- 0.08eV for the energy of EL2. The EL2 electron capture rate is found to have an activation energy of 0.61 +/- 0.08eV which most probably arises from freeze out of conduction electrons. We find the surprising result that emission and capture transients can be seen at temperatures below 200K. Possible reasons for these transients are discussed.