Old English þancian, þoncian "to give thanks, thank, to recompense, to reward," from Proto-Germanic *thankōjanan (source also of Old Saxon thancon, Old Norse þakka, Danish takke, Old Frisian thankia, Old High German danchon, Middle Dutch, Dutch, German danken "to thank"), from *thankoz "thought; gratitude," from PIE root *tong- "to think, feel."
It is related phonetically to think as song is to sing; for sense evolution, compare Old High German minna "loving memory," originally "memory." Also compare related Old English noun þanc, þonc, originally "thought," but also "good thoughts, gratitude." In ironical use, "to blame," from 1550s. To thank (someone) for nothing is recorded from 1703. Related: Thanked; thanking.
mid-13c., plural of thank (n.), from Old English þanc, þonc in its secondary sense "grateful thought, gratitude," from Proto-Germanic *thanka-, from the same root as thank (v.). In prehistoric times the Germanic noun seems to have expanded from "a thinking of, a remembering" to also mean "remember fondly, think of with gratitude." Compare Old Saxon thank, Old Frisian thank, Old Norse þökk, Dutch dank, German Dank. The Old English noun chiefly meant "thought, reflection, sentiment; mind, will, purpose," also "grace, mercy, pardon; pleasure, satisfaction."
As short for I give you thanks from 1580s; often with extensions, such as thanks a lot (1908). Spelling thanx attested by 1907.
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.