The invention relates to a process for producing butadiene from n-butenes which comprises the steps of: A) providing a vaporous n-butenes-comprising input gas stream a1 by evaporating a liquid n-butenes-comprising stream a0; B) introducing the vaporous n-butenes-comprising input gas stream a1 and an at least oxygenous gas into at least one oxidative dehydrogenation zone and oxidatively dehydrogenating n-butenes to butadiene to obtain a product gas stream b comprising butadiene, unconverted n-butenes, steam, oxygen, low-boiling hydrocarbons, high-boiling secondary components, possibly carbon oxides and possibly inert gases, Ca) chilling the product gas stream b by contacting with a cooling medium comprising an organic solvent in at least one chilling zone, the cooling medium being at least partially recycled into the chilling zone, Cb) compressing the chilled product gas stream b which is possibly depleted of high-boiling secondary components in at least one compression stage to obtain at least one aqueous condensate stream c1 and a gas stream c2 comprising butadiene, n-butenes, steam, oxygen, low-boiling hydrocarbons, possibly carbon oxides and possibly inert gases, D) removing noncondensable and low-boiling gas constituents comprising oxygen, low-boiling hydrocarbons, possibly carbon oxides and possibly inert gases as gas stream d2 from the gas stream c2 by absorbing the C4 hydrocarbons comprising butadiene and n-butenes into an absorption medium to obtain a C4-hydrocarbons-laden absorption medium stream and the gas stream d2 and subsequently desorbing the C4 hydrocarbons from the laden absorption medium stream to obtain a C4 product gas stream d1, wherein at least some of the recycled cooling medium from step Ca) is brought into thermal contact with the liquid n-butenes-comprising stream a0 in one or more indirect heat exchangers and at least some of the liquid n-butenes-comprising stream a0 is evaporated by indirect heat transfer with the recycled cooling medium.