The name of artist Tuyoki who worked on the game is Temmie Chang, implying that Temmie is her avatar just as the white Pomeranian is Toby's.
With their strange speech patterns, nonsensical village and generally alien demeanor, the Temmies seem inspired by Mr. Saturn of the Mother series.
It is unknown whether Temmies speak in broken English out of choice or otherwise. Bob the Temmie speaks in lucid, clear English. Shop owner Temmie can swap from "Temmie-speak" to proper English when you annoy her by refusing to trade an item she wants.
Temmie's goofy demeanor and pattern of speaking is probably a reference to the "lolrandom" style of humor and speaking stereotypically exhibited by young teenagers over the internet.