An apparatus (100, 200) for the temperature control of objects, in particular for drying coated vehicle bodies, having a temperature control space with at least one air lock region (115, 117), a fresh air device for producing fresh air which can be fed to the temperature control space, a recirculating air device (114, 110) which removes temperature control space waste air from the temperature control space and produces recirculating air which can be fed to the temperature control space, a feed air device for feeding air to the temperature control space, and a control device, wherein it is possible for a fresh air volumetric flow and a recirculating air volumetric flow to be fed to the feed air device, with the recirculating air device having an afterburning device, it being possible for temperature control space waste air to be fed to the afterburning device for thermal aftertreatment, and the fresh air device comprising a fresh air heat exchanger with a fresh air feed line and a fresh air discharge line, the fresh air discharge line being connected to the feed air device, with the temperature control space defining at least one temperature control space section (T1-T4), with the recirculating air device having, furthermore, at least one temperature control space section heat exchanger which is assigned a temperature control space section (T1-T4) of the temperature control space, the temperature control space section (T1-T4) and the temperature control space section heat exchanger being connected in such a way that temperature control space air can be removed from the temperature control space section (T1-T4), can be guided through the temperature control space section heat exchanger for temperature control purposes, and can be fed to the temperature control space section (T1-T4), and the temperature control space air can thus be fed to the temperature control space section (T1-T4) in a circuit again as a circulating air flow, and the control device being set up to control the fresh air volumetric flow and the recirculating air volumetric flow in such a way that the overall volumetric flow which is fed to the temperature control space and comprises the fresh air volumetric flow and the recirculating air volumetric flow does not undershoot a lower limit, and that a volumetric flow which is introduced into the at least one air lock region (115, 117) is kept constant, with it being possible for the temperature control space air which is temperature controlled by means of the temperature control space section heat exchanger to be fed via a line from the temperature control space section heat exchanger to the feed air device, and/or it being possible for the temperature control space waste air which can be fed to the afterburning device to be fed to the feed air device. a temperature control space with at least one air lock region (115, 117), a fresh air device for producing fresh air which can be fed to the temperature control space, a recirculating air device (114, 110) which removes temperature control space waste air from the temperature control space and produces recirculating air which can be fed to the temperature control space, a feed air device for feeding air to the temperature control space, and a control device, wherein it is possible for a fresh air volumetric flow and a recirculating air volumetric flow to be fed to the feed air device, with the recirculating air device having an afterburning device, it being possible for temperature control space waste air to be fed to the afterburning device for thermal aftertreatment, and the fresh air device comprising a fresh air heat exchanger with a fresh air feed line and a fresh air discharge line, the fresh air discharge line being connected to the feed air device, with the temperature control space defining at least one temperature control space section (T1-T4), with the recirculating air device having, furthermore, at least one temperature control space section heat exchanger which is assigned a temperature control space section (T1-T4) of the temperature control space, the temperature control space section (T1-T4) and the temperature control space section heat exchanger being connected in such a way that temperature control space air can be removed from the temperature control space section (T1-T4), can be guided through the temperature control space section heat exchanger for temperature control purposes, and can be fed to the temperature control space section (T1-T4), and the temperature control space air can thus be fed to the temperature control space section (T1-T4) in a circuit again as a circulating air flow, and the control device being set up to control the fresh air volumetric flow and the recirculating air volumetric flow in such a way that the overall volumetric flow which is fed to the temperature control space and comprises the fresh air volumetric flow and the recirculating air volumetric flow does not undershoot a lower limit, and that a volumetric flow which is introduced into the at least one air lock region (115, 117) is kept constant, with it being possible for the temperature control space air which is temperature controlled by means of the temperature control space section heat exchanger to be fed via a line from the temperature control space section heat exchanger to the feed air device, and/or it being possible for the temperature control space waste air which can be fed to the afterburning device to be fed to the feed air device.