  We report a detailed and comparative study of the single crystal CeCoInGa$_3$
in both experiment and theory. Resistivity measurements reveal the typical
behavior of Kondo lattice with the onset temperature of coherence, $T^*\approx
50\,$K. The magnetic specific heat can be well fitted using a spin-fluctuation
model at low temperatures, yielding a large Sommerfeld coefficient,
$\gamma\approx172\,$mJ/mol K$^2$ at 6 K, suggesting that this is a
heavy-fermion compound with a pronounced coherence effect. The magnetic
susceptibility exhibits a broad field-independent peak at $T_{\chi}$ and shows
an obvious anisotropy within the $bc$ plane, reflecting the anisotropy of the
coherence effect at high temperatures. These are compared with strongly
correlated calculations combining first-principles band structure calculations
and dynamical mean-field theory. Our results confirm the onset of coherence at
about 50 K and reveal a similar anisotropy in the hybridization gap, pointing
to a close connection between the hybridization strength of the low-temperature
Fermi-liquid state and the high-temperature coherence effect.
