The non-isothermal coalescence of two spherical bodies caused by capillary-induced viscous flow was analyzed. Based on this analysis, a new dimensionless number (K number) was introduced for defining thermal coalescence regimes. Based on the value of this number, coalescence may or may not be affected by thermal effects in different cases. To make this clearer, the conventional coalescence models of Frenkel-Eshelby and Pokluda were modified by assuming viscosity as a temperature dependent variable. This was conducted by considering the effects of temperature on the viscosity of the involved material through evaluating different expressions including linear and Reynolds and Williams-Landel-Ferry (WLF) equations. The results of the modified models for the bridge growth rate show that temperature changes significantly affect the kinetics of coalescence, particularly when the characteristic times of coalescence and heat conduction are in the same order, i.e., moderate K numbers. This analysis is applicable for diverse situations since viscous flow coalescence occurs in various physical and industrial applications of particles or droplets.