A numerical thermo-ﬂuid–dynamic study of a compact crossed ﬂows heat exchanger (HX), used to cool the high-pressure oil used in hydraulic circuits of earth-movement industrial vehicles, was performed. The numerical analysis was carried out to verify the inﬂuence of the hydrodynamic regimes of the ﬂuids involved in the heat transfer process, induced by ﬁns in the channels, on the performances of the whole HX. The analysis was developed through three steps of increasing complexity. After a simple model built to evaluate the consistent boundary conditions of temperature, a small scale analysis of the ﬂuid–dynamic phenomena inside the HX was carried out, taking into account geometrical periodical units at oil (OS) and at air side (AS). With the results obtained in this way, the HX performances were evaluated on an overall scale, extrapolating the data up to the real dimensions in terms of heat transfer and pressure loss. With the ‘‘small scale’’ approach at the OS the local heat ﬂux and the pressure losses were quantiﬁed, using a laminar scheme and a high detail in the geometry description of the turbulence generators. With the ‘‘full scale’’ approach, then, simulations were performed considering a porous media with characteristics set up on the previous analysis. The global heat transfer coeﬃcient and the pressure losses were so accounted for. At the AS, the schematization was limited to two periodic portions of the ﬂow and results allowed to evaluate both local and overall heat transfer coeﬃcients. Results were again extrapolated to the real dimensions of the channels.