We present an analysis of the effect of the temperature on the flow of multiphase systems made of multiple miscible components in uniform cylindrical capillaries in adiabatic conditions. The temperature was explicitly included in the dynamic contact angle, tension at the three-phase contact line, and densities and viscosities of the fluids. The mathematical framework accounted for conservative forces (gravity, inertial, and interfacial tensions), nonconservative forces (viscous dissipation), and fluid retardation effects in the reservoirs at the two capillary ends. Temperature-dependent flow regimes ranged from nonoscillatory to oscillatory in a two-phase binary liquid (water-ethanol) system and in a two-phase pure liquid (ether) system. The Ca-Bo orbits highlighted dynamic attractors that depended on specific system characteristics as well as temperature. We conclude that temperature alone expresses and important role in the dynamical characteristics of capillary rise flow around its equilibrium.