HTS dynamo-type ‘flux pumps’ can inject large DC currents into a closed superconducting circuit. Here we report results from an experimental variable-temperature HTS dynamo in which the stator is formed by wrapping a 46 mm tape of HTS coated conductor in a cylindrical drum around a mechanical rotor. This continuous stator topology results in a high current device that can inject >1 kA into a series-connected HTS coil at 53 K. We observe that the open-circuit DC output voltage (V_oc), attains its maximum value at a temperature only ∼5 K lower than the stator T_c. At lower temperatures V_oc decreases steadily, and falls to zero below ∼ 40 K. This behaviour can be explained through finite element modelling using the T-A approach which utilises measured values for the temperature and B-field dependence of J_c for the HTS tape.  At higher temperatures almost all of the applied flux penetrates the stator tape leading to a locally-induced emf at all times. However, as temperature decreases, the magnitude of screening currents flowing in the tape increases, and these eventually completely shield flux from penetrating the tape. At this point the locally-induced emf within the stator tape becomes zero, and this means that the time-averaged DC output from the dynamo must also be zero. A key implication that can be drawn from our results is that any HTS flux pumps which relies on flux penetration of a film should be operated at temperatures well above their flux-screening point. This should be a key design consideration in the future development of multi-kA class HTS flux pumps.