We demonstrate that the dissociative recombination of D2H+ with low-energy electrons depends on the rotational energy of the molecular ion such that highly excited ions have a larger rate coefficient than colder ones. Observations on an ion beam continuously interacting with electrons at low relative velocity indicate that excited rotational levels are preferentially depleted which, in competition with radiative heating due to blackbody radiation, provides an opportunity for controlling the rotational temperature of stored molecules.