CeNi1−xCux is a substitutional magnetic system where the interplay of the different magnetic interactions leads to the disappearance of the long-range magnetic order on the CeNi side. The existence of inhomogeneities (spin clusters or phase coexistence) has been previously detected by magnetization and muon spin relaxation (μSR) spectroscopy measurements. These inhomogeneities are always observed regardless of the different preparation methods and must, then, be considered as intrinsic. We present a detailed specific heat study in a large temperature range of 0.2 to 300 K. The analysis of these data, considering also previous neutron scattering, magnetic characterization, and μSR results, allows us to present a convenient description of the system as inhomogeneous on the nanometric scale. Two regimes are detected in the compositional range depending on the dominant Ruderman-Kittel-Kasuya-Yosida or Kondo interactions. We propose that the long-range magnetic order at low temperatures is achieved by a percolative process of magnetic clusters that become static below the freezing temperature Tf. In this scenario the existence of a quantum critical point at the magnetic-nonmagnetic crossover must be discarded. This situation should be considered as an example for other substitutional compounds with anomalous magnetic or superconducting properties.