  We investigate a non-isothermal diffuse-interface model that describes the
dynamics of two-phase incompressible flows with thermo-induced Marangoni
effect. The governing PDE system consists of the Navier--Stokes equations
coupled with convective phase-field and energy transport equations, in which
the surface tension, fluid viscosity and thermal diffusivity are temperature
dependent functions. First, we establish the existence and uniqueness of local
strong solutions when the spatial dimension is two and three. Then in the two
dimensional case, assuming that the $L^\infty$-norm of the initial temperature
is suitably bounded with respect to the coefficients of the system, we prove
the existence of global weak solutions as well as the existence and uniqueness
of global strong solutions.
