Is the thermal conductivity of metals affected by magnetic fields?

Magnetic fields certainly can influence thermal conductivity. This shows up, not surprisingly, when there is a strong influence of the magnetic field on other properties, particularly electronic ones.

One (non-metal) example is 'Thermal conductivity tensor in YBa$_{2}$Cu$_{3}$O$_{7-x}$: Effects of a planar magnetic field' by R. Ocana and P. Esquinazi, Phys Rev B66 064525 (2002). The influence of magnetic fields on the superconducting state is well known, so you could easily see they could mess with the pairing states and change the (primarily electronic) thermal conductivity at low temperatures.

Another example is 'Giant Magnetic Field Effect on Thermal Conductivity of Magnetic Multilayers, Cu/Co/Cu/Ni(Fe)', H. Sato et al., J. Phys. Soc. Jpn. 62 431-434 (1993). Again, the magnetic interactions that lead to the large magnetoresistance changes should, and can, impact the electronic component of the thermal conductivity.

As a final example, 'Effect of a magnetic field on the thermal conductivity of lead telluride-tin telluride', T. Knittel and H. J. Goldsmid, J. Phys. C. 12 1891-1897 (1979). Again, at low temperature, the electronic thermal conductivity dominates, and the magnetic field will modulate it.