Apparatus for controlling the temperature of a reactor in which an exo- or endothermic reaction can be conducted in a reaction medium, wherein the apparatus comprises a reactor, a heat exchanger system, a circulation vessel containing a temperature control fluid with which the heat exchanger system is fed, and a pump with which the temperature control fluid is returned via a conduit to the heat exchanger system and via a conduit to the circulation vessel, and with which the volume of temperature control fluid in the temperature control circuit is adjusted, wherein the heat exchanger system comprises at least one temperature control finger, wherein the temperature control finger is a double tube consisting of an inner tube through which a temperature control fluid is introduced into the double tube and an outer tube which is in direct contact with the reaction medium and in which the return flow of the temperature control fluid is in the annular gap between inner tube and outer tube, wherein the heat exchanger system is recessed into the reactor such that the outer tube(s) of the temperature control finger are in contact with the reaction medium, characterized in that the inner tube of the double tube is thermally insulated and in that the apparatus has a first shut-off fitting with which the temperature control fluid pressure can be adjusted, a second shut-off fitting with which the temperature of the temperature control fluid can be monitored and controlled, and at least two temperature measurement devices (17, 18) for measuring the internal reactor temperature, wherein the first shut-off fitting is mounted on the conduit that leads to the circulation vessel; wherein the second shut-off fitting is present in an outlet conduit of the circulation vessel, by means of which steam or liquid can be discharged; and wherein the temperature of the temperature control fluid is controlled as a function of an internal reactor temperature. wherein the heat exchanger system comprises at least one temperature control finger, wherein the temperature control finger is a double tube consisting of an inner tube through which a temperature control fluid is introduced into the double tube and an outer tube which is in direct contact with the reaction medium and in which the return flow of the temperature control fluid is in the annular gap between inner tube and outer tube, wherein the heat exchanger system is recessed into the reactor such that the outer tube(s) of the temperature control finger are in contact with the reaction medium, characterized in that the inner tube of the double tube is thermally insulated and in that the apparatus has a first shut-off fitting with which the temperature control fluid pressure can be adjusted, a second shut-off fitting with which the temperature of the temperature control fluid can be monitored and controlled, and at least two temperature measurement devices (17, 18) for measuring the internal reactor temperature, wherein the first shut-off fitting is mounted on the conduit that leads to the circulation vessel; wherein the second shut-off fitting is present in an outlet conduit of the circulation vessel, by means of which steam or liquid can be discharged; and wherein the temperature of the temperature control fluid is controlled as a function of an internal reactor temperature.