Quantum spin liquids (QSLs) are intriguing phases of matter possessing fractionalized excitations. Several quasi-two-dimensional materials have been proposed as candidate QSLs, but direct evidence for fractionalization in these systems is still lacking. In this paper, we show that the interplane thermal conductivity in layered QSLs carries a unique signature of fractionalization. We examine several types of gapless QSL phases - a Z₂ QSL with either a Dirac spectrum or a spinon Fermi surface, and a U(1) QSL with a Fermi surface - and consider both clean and disordered systems. In all cases, the in-plane and c-axis thermal conductivities have a different power-law dependence on temperature because of the different mechanisms of transport in the two directions: In the planes, the thermal current is carried by fractionalized excitations, whereas the interplane current is carried by integer (nonfractional) excitations. In layered Z₂ and U(1) QSLs with a Fermi surface, and in the disordered Z₂ QSL with a Dirac dispersion, the c-axis thermal conductivity is parametrically smaller than the in-plane one but parametrically larger than the phonon contribution at low temperatures.