misthink v.

prefix of Germanic origin affixed to nouns and verbs and meaning "bad, wrong," from Old English mis-, from Proto-Germanic *missa- "divergent, astray" (source also of Old Frisian and Old Saxon mis-, Middle Dutch misse-, Old High German missa-, German miß-, Old Norse mis-, Gothic missa-), perhaps literally "in a changed manner," and with a root sense of "difference, change" (compare Gothic misso "mutually"), and thus possibly from PIE *mit-to-, from root *mei- (1) "to change."

Productive as word-forming element in Old English (as in mislæran "to give bad advice, teach amiss"). In 14c.-16c. in a few verbs its sense began to be felt as "unfavorably," and it came to be used as an intensive prefix with words already expressing negative feeling (as in misdoubt). Practically a separate word in Old and early Middle English (and often written as such). Old English also had an adjective (mislic "diverse, unlike, various") and an adverb (mislice "in various directions, wrongly, astray") derived from it, corresponding to German misslich (adj.). It has become confused with mis- (2).

Old English þencan "imagine, conceive in the mind; consider, meditate, remember; intend, wish, desire" (past tense þohte, past participle geþoht), probably originally "cause to appear to oneself," from Proto-Germanic *thankjan (source also of Old Frisian thinka, Old Saxon thenkian, Old High German denchen, German denken, Old Norse þekkja, Gothic þagkjan).

Old English þencan is the causative form of the distinct Old English verb þyncan "to seem, to appear" (past tense þuhte, past participle geþuht), from Proto-Germanic *thunkjan (source also of German dünken, däuchte). Both are from PIE *tong- "to think, feel" which also is the root of thought and thank.

The two Old English words converged in Middle English and þyncan "to seem" was absorbed, except for its preservation in archaic methinks "it seems to me."

As a noun, think, "act of prolonged thinking," is attested by 1834. The figurative thinking cap is attested from 1839.