A high sensitivity fiber optic temperature sensor based on a side-polished fiber (SPF) coupled to a tapered multimode overlay waveguide (MMOW) is proposed and studied. Both tapered and non-tapered MMOW were considered to study the effect of tapering of MMOW on the characteristics of the device and to investigate the criticality of the uniformity of the multimode overlay waveguide over the SPF. Present study shows that tapering of the MMOW can be used to tune the desired wavelength range without any loss in the sensitivity. Sensitivity up to 9 nm/$^{circ}C$ within the temperature range of 25 to $100^{circ}C$ can be achieved with the proposed sensor, almost 6 times higher compared even to state-of-the-art high-sensitivity grating-based fiber optic temperature sensors.