The quadrupole Kondo effect describes an exotic state of matter that is related to non-Fermi liquid behavior and residual entropy. A promising class of materials to explore this unconventional hybridization phenomenon is the group of cubic Pr-based 1-2-20 systems with a quadrupolar non-Kramers ground state doublet. Even though the thermodynamic characteristics of the quadrupole Kondo effect have been theoretically well established, it is yet unknown how the effect manifests itself in the thermal expansion, magnetostriction and Grüneisen ratio. In order to uncover a possible link between aforementioned thermodynamic probes and the quadrupole Kondo effect, this thesis focuses on low temperature dilatometric measurements on the quadrupole Kondo lattice PrIr2Zn20 and the single-impurity quadrupole Kondo candidate material Y1-xPrxIr2Zn20
