Yes, the thermal boundary layer exists because of combination of diffusion of energy by liquid particles(the rate is determined the thermal diffusivity of the liquid), and the so-called convective heat transfer due to the movement of liquid particles(momentum diffusion),which exchange the thermal energy between adjacent layers of particles.
The magnitudes of these two diffusion mechanisms are compared using Pr number, which is v/a. v is the kinematic viscosity, and a is thermal diffusivity.
If there is no flow, then there is only thermal diffusion existing, e.g., purely heat conduction.
The length of any diffusion is L = (k*t)^0.5, where k is general diffusivity with unit of m^2/s, and t is time: the physical meaning is for a given time, such diffusion happens within a length of L defined by above equation.
So for momentum boundary layer thickness delta_m is around (v*t)^0.5, while here t = L/V, v is kinematic viscosity,L is the plate length and V is the coming velocity, so delta_m ~ (v*L/V)^0.5, which is the same expression usually derived from any textbooks.
Since thermal boundary layer is partly because of momentum boundary, it's must be a function of both Re and Pr numbers.