In this chapter, we shall take a closer look at the transport of entropy. Simple aspects will be introduced that go beyond what we already studied in Chapter 4 (Section 4.6). This extends the treatment of thermal processes into the realm of phenomena which are missing from the theory of the thermodynamics of ideal fluids (Chapter 5). Many texts on thermodynamics and on heat transfer sharply distinguish between the two subjects, which only emphasizes that a unified presentation of all thermal phenomena is called for. While we will not achieve the stated goal in this chapter, the ground will be prepared for a theory of continuum thermodynamics of which we will get a first glimpse in Part III.