1540s, "a leading, guidance" (a sense now obsolete), from French conduction "hire, renting," and directly from Latin conductionem (nominative conductio), noun of action from past-participle stem of conducere "to lead or bring together," from assimilated form of com "with, together" (see con-) + ducere "to lead" (from PIE root *deuk- "to lead").
Sense of "a conducting through a channel" is from 1610s in reference to liquids; in physics, "transmission, conveyance" of heat, etc., from 1814.
mid-15c., renten, "to rent out property, grant possession and enjoyment of in exchange for a consideration paid in the nature of rent," from Old French renter "pay dues to," or from rent (n.1). Related: Rented; renting.
Earlier (mid-14c.) it was used in the more general sense of "provide with revenue, endow with income." The sense of "to take and hold in exchange for rent" is from 1520s. The intransitive sense of "be leased for rent" is from 1784.
Prefix rent-a- is attested by 1921, mainly of businesses that rented various makes of car (Rentacar is a trademark registered in U.S. 1924); extended to other "temporary" uses since 1961.