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 Gruneisen 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 $Brightarrow 0$ 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.
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