Efficiently tuning the output intensity of an optical device is of vital importance for the establishment of optical interconnects and networks. Thermo-optical modulation is an easily implemented and convenient approach and has been widely employed in photonic devices. In this paper, we proposed a novel thermo-optical modulator based on a microfiber knot resonator (MKR) and graphene heater. Upon applying voltage to graphene, the resonant property of the MKR could be thermally tuned with a maximum phase shift of 2.1π. Intensity modulation shows a fast optical response time thanks to the high thermal conductivity of graphene and the thin microfiber diameter of the MKR.