The prototype detector of the ICAL experiment at the India-based Neutrino Observatory, the mini-ICAL was operational at the IICHEP, Madurai. A Cosmic Muon Veto detector (CMVD) around the mini-ICAL was planned using extruded plastic scintillators with embedded WLS fibers. A similar system is being commissioned at TIFR. The SiPM is used as a photo-transducer and that will be calibrated using an ultrafast LED driver. Other than the basic efficiency and gain study for the CMVD as a function of overvoltage (V \(_{ov}\) ), an experimental setup was designed to characterise the SiPMs in a temperature-controlled environment. The readout electronics involves trans-impedance amplifiers of combined gain 1.24 mV/ \(\upmu \) A and a digital storage oscilloscope for the data collection without much distortion of SiPM signal. From the point of view of avalanche formation, the rise time of the SiPM signals should be independent of the temperature and some extent with the operational overvoltage (V \(_{ov}\) ), but the observations show variations as a function of those two parameters. Various characteristics of the signal shape, recovery time etc. were studied as a function of V \(_{ov}\) and the ambient temperature. This paper will cover the details of those results and possible explanations of those variations.