An electrical machine (1) has a rotor (3) and a stator (2). The rotor (3) is actively connected with a rotor shaft (4), which is rotationally mounted in a housing (7) by means of at least one bearing (5), in particular a roller bearing. The electrical machine has an efficient cooling system that is easy and economical to construct by locating the bearing (5) in a bearing end plate (6). The bearing end plate (6) is provided with at least one coolant space (15; 17; 23) that carries a coolant flow.