"starve" used to mean "freeze to death", actually. from etymonline:
O.E. steorfan "to die" (pt. stearf, pp. storfen), from P.Gmc. *sterban "be stiff" (cf. O.Fris. sterva, Du. sterven, O.H.G. sterban "to die," O.N. stjarfi "tetanus"), from PIE base *ster- "stiff, rigid" (cf. Gk. sterphnios "stiff, rigid," sterphos "hide, skin," O.C.S. strublu "strong, hard;" see stare). The conjugation became weak in Eng. by 16c. The sense narrowed to "die of cold" (14c.); meaning "to kill with hunger" is first recorded 1530 (earlier to starve of hunger, 1124). Intrans. sense of "to die of hunger" dates from 1578. Ger. cognate sterben retains the original sense of the word, but the Eng. has come so far from its origins that starve to death (1910) is now common. Starvation (1778) is a hybrid, with a L. ending, apparently first used in ref. to British policies toward rebellious New England colonies.
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O.E. steorfan "to die" (pt. stearf, pp. storfen), from P.Gmc. *sterban "be stiff" (cf. O.Fris. sterva, Du. sterven, O.H.G. sterban "to die," O.N. stjarfi "tetanus"), from PIE base *ster- "stiff, rigid" (cf. Gk. sterphnios "stiff, rigid," sterphos "hide, skin," O.C.S. strublu "strong, hard;" see stare). The conjugation became weak in Eng. by 16c. The sense narrowed to "die of cold" (14c.); meaning "to kill with hunger" is first recorded 1530 (earlier to starve of hunger, 1124). Intrans. sense of "to die of hunger" dates from 1578. Ger. cognate sterben retains the original sense of the word, but the Eng. has come so far from its origins that starve to death (1910) is now common. Starvation (1778) is a hybrid, with a L. ending, apparently first used in ref. to British policies toward rebellious New England colonies.