You're looking through the wrong end of the telescope. The exchanger is removing the heat from the fuel not adding it to the freon. Well, actually it IS adding heat to the freon but the cooling system is designed to dissipate the heat whereas the fuel system is not.

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“Whatever story you're telling, it will be more interesting if, at the end you add, "and then everything burst into flames.”
― Brian P. Cleary, You Oughta Know By Now