The Properties of Gases and Liquids 5th Edition by Bruce E. Poling, John M. Prausnitz , John P. O'Connell is an excellent place to start. A shorter and less comprehensive discussion is in Transport Phenomena by Bird, Stewart and Lightfoot.

There are textbooks on conductive heat transfer such as 

[Latif M. Jiji. Heat Conduction, 3rd Edition. Springer, 2009] or [Liqiu Wang, Xuesheng Zhou, Xiaohao Wei. Heat Conduction. Mathematical Models and Analytical Solutions.  Springer, 2008].

If you are interested in physical mechanisms of thermal conductivity, you need to look through literature on materials science. For example, [Philip Hofmann. Solid State Physics. An Introduction, Second Edition. Wiley-VCH, 2015] or [James Patterson, Bernard Bailey. Solid-State Physics Introduction to the Theory, Second Edition. Springer, 2007]. This discipline includes some math which may not be that easy.  The simplest intro I can think of is [Sharon Ann Holgate. Understanding solid state physics. CRC Press, 2010]

PS Precisely speaking, thermal conductivity is not the subject of engineering thermodynamics which studies equilibrium systems. In this case heat fluxes are infinitely small, and thermal conductivity is ignored. 

thank you very much for this helpful, detailed answers! 

John H Lienhard IV and John H Lienhard V, 'A Heat Transfer Textbook', Third Edition, Phlogyston Press, Cambridge, Massachusetts 

thank you too, Penka Zlateva!