CdTe is increasingly being used as the x-ray sensing material in imaging pixel array detectors for x-rays, generally above 20 keV, where silicon sensors become unacceptably transparent. Unfortunately CdTe suffers from polarization, which can alter the response of the material over time and with accumulated dose. Most prior studies used long integration times or CdTe that was not of the hole-collecting Schottky type. We investigated the temporal response of hole-collecting Schottky type CdTe sensors on timescales ranging from tens of nanoseconds to several seconds. We found that the material shows signal persistence on the timescale of hundreds of milliseconds attributed to the detrapping of a shallow trap, and additional persistence on sub-microsecond timescales after polarization. The results show that this type of CdTe can be used for time resolved studies down to approximately 100 ns. However quantitative interpretation of the signal requires careful attention to bias voltages, polarization and exposure history. © 2017 IOP Publishing Ltd and Sissa Medialab.