Polymer optical fibre (POF) temperature sensors are rapidly replacing conventional temperature sensors owing to their unique and attractive features, such as small size, immunity to electromagnetic interference, multiplexing, and remote sensing capabilities. The recent developments in temperature sensing using polymer optical fibres are presented. Polymer optical fibre (POF) temperature sensors of various types: macro-bend fibre sensors, microfibre resonators, fibre Bragg grating, Fabry-Perot interferometers, and POF sensors coated with zinc oxide nanorods are discussed. This study also includes dual-parameter sensors to demonstrate intrinsic sensitivities of polymer fibres to temperature, relative humidity, and strain. The prospects and challenges of POF temperature sensors in the automotive industry, biomedical sector, chemical industry, and electrical power applications are also highlighted. This review aims to help researchers in this field identify areas of further work towards improving the accuracy and operating range of POF temperature sensors.