As far as heat conduction goes, it is pretty much the same for solids and fluids in general in continous media. What really change is the constitutive relation for the heat flux vector for a given material. In most cases one is interested in Fourier materials which obey
(1) h = -K grad(T) ,
where h is the heat flux vector, K is a second order positive semi-definite tensor field called thermal conductivity and T is the temperature. See
lecture 7 'The Onsager Relations' of C.A.Truesdell's Rational thermodynamics
and also
W. A. Day & M. E. Gurtin's 'On the Symmetry of the Conductivity Tensor and other Restrictions in the Non Linear Theory of Heat Conduction'
paper considering material simmetries for K. Other good paper is
B. D. Coleman & V. J. Mizel's 'Thermodynamics and Departures from Fourier's Law of Heat conduction'
There is a main mechanism heat transfer it's a molecular exchange. I'm recommend to you a paper in this region: Gladkov S.O. Solid State Communications 1995. V.94. N9. PP.789-791.