WordNet records no synonym and no antonym for simmer. It is the only member of each of its synsets, which is common for technical, taxonomic and single-sense vocabulary — there is no other English word that means the same thing. The broader and narrower terms below are the useful relations in that case.
Counts are distinct word forms across every sense. A synonym that appears under three senses is counted once here and shown three times below, under each sense it belongs to.
temperature just below the boiling point
“the stew remained at a simmer for hours”
boil slowly at low temperature
“simmer the sauce”
Synonyms, antonyms and the broader and narrower relations for simmer come from Princeton University’s WordNet. Full sources and licences.