A process for polymerizing ethylene or copolymerizing ethylene and one or more C 3 -C 12 -1-alkenes in a slurry polymerization at temperatures of from 40 to 150°C and pressures from 0.1 to 5 MPa in the presence of a polymerization catalyst, wherein the process is carried out in a reactor system comprising - a polymerization reactor configured to have a content in liquid form; - an agitator for agitating the reactor content; - one or more first heat exchangers located outside the polymerization reactor for cooling or heating the reactor content; - one or more circulation pumps for withdrawing the reactor content from the polymerization reactor and circulating the reactor content through the one or more first heat exchangers; and - a closed loop of a tempering medium for cooling or heating the one or more first heat exchangers, which closed loop is equipped with a second heat exchangers for cooling the tempering medium and is equipped with a third heat exchangers for heating the tempering medium, and wherein, during the polymerization of ethylene or copolymerizing ethylene and the one or more C 3 -C 12 -1-alkenes, - the polymerization reactor is filled with a slurry of ethylene polymer particles in a liquid medium comprising a hydrocarbon diluent; - the slurry is cooled by withdrawing slurry from the polymerization reactor, cooling the slurry in the one or more first heat exchangers and returning the cooled slurry to the polymerization reactor; - the temperature of the tempering medium cooling the one or more first heat exchangers is in the range from 20°C to 50°C; and - the tempering medium is cooled in the second heat exchanger by a coolant having a temperature from -20° to 45°C. wherein the process is carried out in a reactor system comprising - a polymerization reactor configured to have a content in liquid form; - an agitator for agitating the reactor content; - one or more first heat exchangers located outside the polymerization reactor for cooling or heating the reactor content; - one or more circulation pumps for withdrawing the reactor content from the polymerization reactor and circulating the reactor content through the one or more first heat exchangers; and - a closed loop of a tempering medium for cooling or heating the one or more first heat exchangers, which closed loop is equipped with a second heat exchangers for cooling the tempering medium and is equipped with a third heat exchangers for heating the tempering medium, and - a polymerization reactor configured to have a content in liquid form; - an agitator for agitating the reactor content; - one or more first heat exchangers located outside the polymerization reactor for cooling or heating the reactor content; - one or more circulation pumps for withdrawing the reactor content from the polymerization reactor and circulating the reactor content through the one or more first heat exchangers; and - a closed loop of a tempering medium for cooling or heating the one or more first heat exchangers, which closed loop is equipped with a second heat exchangers for cooling the tempering medium and is equipped with a third heat exchangers for heating the tempering medium, and wherein, during the polymerization of ethylene or copolymerizing ethylene and the one or more C 3 -C 12 -1-alkenes, - the polymerization reactor is filled with a slurry of ethylene polymer particles in a liquid medium comprising a hydrocarbon diluent; - the slurry is cooled by withdrawing slurry from the polymerization reactor, cooling the slurry in the one or more first heat exchangers and returning the cooled slurry to the polymerization reactor; - the temperature of the tempering medium cooling the one or more first heat exchangers is in the range from 20°C to 50°C; and - the tempering medium is cooled in the second heat exchanger by a coolant having a temperature from -20° to 45°C. - the polymerization reactor is filled with a slurry of ethylene polymer particles in a liquid medium comprising a hydrocarbon diluent; - the slurry is cooled by withdrawing slurry from the polymerization reactor, cooling the slurry in the one or more first heat exchangers and returning the cooled slurry to the polymerization reactor; - the temperature of the tempering medium cooling the one or more first heat exchangers is in the range from 20°C to 50°C; and - the tempering medium is cooled in the second heat exchanger by a coolant having a temperature from -20° to 45°C.