The invention relates to a bioreactor, in particular a fermentation reactor, comprising a cylindrical reactor tank (1) with a vertical axis (1') and an agitator (3), arranged in a flow conducting pipe (2) and substantially delivering the flow vertically downwards, and also a heat exchanger (4), arranged in the reactor tank (1). According to the invention, the heat exchanger (4) is arranged in the region of the outlet opening (11) of the flow conducting pipe (2) and has in relation to the vertical axis (1') of the reactor tank (1) radially outwardly directed flow elements (10).