One of the greatest fallacies in the physiology is the paradigm that the immediate exercise hyperemia could be governed by the arteriolar dilation. Striated muscle cells represent thermal engines with internal combustion, which must be cooled and thermo-regulated, like every man-made one, individually, not in bulk. These cells are extremely vulnerable to overheating, since they can increase their energy production enormously in far less than a second anaerobically (humming bird makes 80 wing-beats/sec). They have not intracellular convective heat transfer, since about 80% of their water is entrapped in the myofibrils. For that, more than other cells, they need an immediate response of their external cooling, in order not to raise their surface temperature, which would hamper the rapid elevation of the intracellular temperature gradient (2) determining their internal conductive heat transfer. This is especially valid for the white muscle cells, with their great anaerobic loading, which would first expand and die from overheating (1). That’s why we tested our hypothesis that CO2 plays decisive role in the homeotherms’ thermo-baric homeostasis, allowing coupling the capillary blood flow with the positive temperature gradient between their adherent cells and the capillary blood, which proves the latter’s primary cooling role. For that we measured the thermo-baric relationship of CO2 dissolved in saline for different concentrations and plotted pressure against temperature. We discovered that in each diagram (Fig. 1) there are several inflex points and that the first derivatives of all of them (Fig. 2) have one maximum always near the 37 deg C, independently from the CO2 content. Thus, we discovered a physical constant, explaining the human rest body core temperature, auto-regulated by the increased curve slope at this point. For that we created the following theory: a) The capillary blood flow is promoted using the Malone heat engine-cycle; b) The working medium is the containing dissolved CO2 blood plasma, expanding by all factors reducing the CO2 solubility in it or producing additional amounts of CO2, like cell metabolism (anaerobic-5-6 times greater) or acids; c) The capillary glycocalyx molecular-chains (bended toward the venous limb by the erythrocyte passage) and the parachute-formed erythrocytes act as ratchet and pawl, determining their one-way motion e. g.. a capillary pump; d) The plasma expands due to the nanobubbles formed at the liquid/solid interfaces at the glycocalyx molecular-chains, their density reaching maximum at 37 deg C and decreasing at a higher temperature (4, 5). This pumping explains the inflammation, as well (3). Since muscle contractions cause mechanically capillary pressure elevation with a net positive effect by the “ratchet” system, we suggest an additional term “capillary muscle pump”.