  Dwarf planets Eris and Makemake have surfaces bearing methane ice of unknown
origin. D/H ratios were recently determined from James Webb Space Telescope
(JWST) observations of Eris and Makemake, giving us new clues to decipher the
origin of methane. Here, we develop geochemical models to test if the origin of
methane could be primordial, derived from CO$_2$ or CO ("abiotic"), or sourced
by organics ("thermogenic"). We find that primordial methane is inconsistent
with the observational data, whereas both abiotic and thermogenic methane can
have D/H ratios that overlap the observed ranges. This suggests that Eris and
Makemake either never acquired a significant amount of methane during their
formation, or their original inventories were removed and then replaced by a
source of internally produced methane. Because producing abiotic or thermogenic
methane likely requires temperatures above ~150{\deg}C, we infer that Eris and
Makemake have rocky cores that underwent substantial radiogenic heating. Their
cores may still be warm/hot enough to make methane. This heating could have
driven hydrothermal circulation at the bottom of an ice-covered ocean to
generate abiotic methane, and/or metamorphic reactions involving accreted
organic matter could have occurred in response to heating in the deeper
interior, generating thermogenic methane. Additional analyses of relevant
thermal evolution model results and theoretical predictions of the D/H ratio of
methane in the solar nebula support our findings of elevated subsurface
temperatures and an apparent lack of primordial methane on Eris and Makemake.
It remains an open question whether their D/H ratios may have evolved
subsequent to methane outgassing. Recommendations are given for future
activities to further test proposed scenarios of abiotic and thermogenic
methane production on Eris and Makemake, and to explore these worlds up close.
