Previously unresolved three-dimensional aspects of the time mean, as well as the annual and semiannual cycles of the heat transport, are studied in the Gulf of California using a minimal box model suggested by the hydrographic data. At the very least three horizontal domains are needed for the model: a shallow region north of the big islands, a deep region identifiable with the Ballenas Channel, and another deep region spanning the rest of the gulf south of the archipelago. Only one vertical layer is considered in the northern region, whereas two layers are taken into account in the other two regions. Out of all of the possible heat exchanges among the various boxes of the model, the least-flux-variance solution is considered. The annual mean heat entering the surface in the northern region is exported in almost equal amounts to the Ballenas Channel and the southern region. Ballenas Channel, in turn, exports heat to the southern region mainly through the lower layer, producing a transversal asymmetry of the mouthward flux into the upper layer. At the mouth the heat is exported to the Pacific Ocean largely through the upper layer. Both the annual and semiannual amplitude of the exchanges between all regions are as important as the annual average, except at the mouth of the gulf, where the semiannual component is not statistically relevant. The Pacific Ocean fluxes estimates at the annual frequency agree well with those produced by a baroclinic wave, which has been shown to explain a big deal of the thermodynamics of the gulf. The annual mean vertical flux per unit horizontal area in the Ballenas Channel is much larger than that in the southern region. This reinforces previous speculations that mixing processes in this region are very important. A depth-independent eddy diffusivity parameterization suggests that diffusion might not be invoked to explain the annual mean vertical flux in the Ballenas Channel. ¿ 2000 American Geophysical Union