  YbCo$_2$Ge$_4$ is a clean paramagnetic Kondo lattice which displays non-Fermi
liquid behavior. We report a detailed investigation of the specific heat,
magnetic Gr\"uneisen parameter ($\Gamma_{\rm mag}$) and temperature derivative
of the magnetization ($M$) on a high-quality single crystal at temperatures
down to $0.1$~K and magnetic fields up to 7~T. $\Gamma_{\rm mag}$ and $dM/dT$
display a divergence upon cooling and obey $T/B$ scaling. Similar behavior has
previously been found in several other Yb-based Kondo lattices and related to a
zero-field quantum critical point without fine tuning of pressure or
composition. However, in the approach of $B\rightarrow 0$ the electronic heat
capacity coefficient of YbCo$_2$Ge$_4$ saturates at low $T$, excluding
ferromagnetic quantum criticality. This indicates that $T/B$ scaling is
insufficient to prove a zero-field quantum critical point.
