This study proposes a thermal sensor based on whispering gallery modes (WGMs) in a polymer core optical ring resonator (PCORR). The thermal sensitivity and detection limit (i.e., the temperature resolution) for WGMs of various orders and polarizations are theoretically studied as a function of the ring wall thickness. The results show that the temperature detection limits can be as low as $4\times {10}^{-5}$ and $6\times {10}^{-6}\mathrm{K}$ for laser linewidths of 2 and $0.3\mathrm{MHz}$ , respectively. The ultrahigh temperature resolution makes the PCORR a very promising platform for temperature measurement. The analysis also shows that the WGM of a lower order has better thermal sensing performance and a thinner optimal thickness of the ring resonator.