High time resolution optical/Infrared (IR) astronomy will require fast response detectors. In order to meet such requirement, cryogenic optical/IR detectors, such as superconducting tunnel junctions (STJ) and transition-edge sensors (TES), are under development. Of these cryogenic detectors, superconducting titanium (Ti) bolometric detectors, with a transition temperature of around 300 mK, based on the electronphonon decoupling mechanism, is promising in fast response. In this paper, we report on the characterization of electro-thermal properties of a small-size (1 µm × 1 µm × 37 nm) superconducting Ti detector. The low frequency noise of Ti film was fitted by empirical Hooge model. A discrepancy between the Hooge constant of the Ti film and that of normal metals shows disorder in the Ti film. Thermal conductance was estimated extracted via measured current-voltage curves at different bath temperatures. The time constant was calculated as tens of nanoseconds, which was quite fast faster than expected. The fast response potentially enables the high speed optical/IR astronomical observations. Detailed experimental and analytical results are presented.