The influences of the diameter (size) of single-walled carbon nanotubes (SWCNTs) and the temperature on the viscosity of water confined in SWCNTs are investigated by an "Eyring-MD" (molecular dynamics) method. The results suggest that the relative viscosity of the confined water increases with increasing diameter and temperature, whereas the size-dependent trend of the relative viscosity is almost independent of the temperature. Based on the computational results, a fitting formula is proposed to calculate the size- and temperature- dependent water viscosity, which is useful for the computation on the nanoflow. To demonstrate the rationality of the calculated relative viscosity, the relative amount of the hydrogen bonds of water confined in SWCNTs is also computed. The results of the relative amount of the hydrogen bonds exhibit similar profiles with the curves of the relative viscosity. The present results should be instructive for understanding the coupling effect of the size and the temperature at the nanoscale.