A temperature control system, comprising: a heat medium circuit that connects, with a pipe, a heat source device that is controlled to perform either heating or cooling of a heat medium flowing therein and allow the heat medium to flow out therefrom, a heat exchange device that exchanges heat with a subject to be temperature-controlled by allowing the heat medium to pass therethrough, to thereby control a temperature of the subject to be controlled to a target temperature, and a conveying device that conveys the heat medium, the heat medium circuit circulating the heat medium therein with the conveying device; a controller that controls, through the control of the heat source device, a temperature of the heat medium flowing out from the heat source device, and an outside air temperature sensor that detects an outside air temperature, characterised in that: the controller is configured to perform a first control that controls the temperature of the heat medium flowing out of the heat source device on a basis of the outside air temperature and a temperature difference between chronologically preceding and following outside air temperatures, to thereby control the temperature of the subject to be controlled to be the target temperature, wherein the controller is configured to use, when executing the first control, a temperature difference between a temperature at a past time of the subject to be controlled and an outside air temperature of the past time, and a temperature difference between an inflow temperature at the past time and an outflow temperature at the past time of the heat medium that had flowed into and out of the heat source device, in addition to the outside air temperature and the temperature difference between the chronologically preceding and following outside air temperatures. a heat medium circuit that connects, with a pipe, a heat source device that is controlled to perform either heating or cooling of a heat medium flowing therein and allow the heat medium to flow out therefrom, a heat exchange device that exchanges heat with a subject to be temperature-controlled by allowing the heat medium to pass therethrough, to thereby control a temperature of the subject to be controlled to a target temperature, and a conveying device that conveys the heat medium, the heat medium circuit circulating the heat medium therein with the conveying device; a controller that controls, through the control of the heat source device, a temperature of the heat medium flowing out from the heat source device, and an outside air temperature sensor that detects an outside air temperature, characterised in that: the controller is configured to perform a first control that controls the temperature of the heat medium flowing out of the heat source device on a basis of the outside air temperature and a temperature difference between chronologically preceding and following outside air temperatures, to thereby control the temperature of the subject to be controlled to be the target temperature, wherein the controller is configured to use, when executing the first control, a temperature difference between a temperature at a past time of the subject to be controlled and an outside air temperature of the past time, and a temperature difference between an inflow temperature at the past time and an outflow temperature at the past time of the heat medium that had flowed into and out of the heat source device, in addition to the outside air temperature and the temperature difference between the chronologically preceding and following outside air temperatures. the controller is configured to perform a first control that controls the temperature of the heat medium flowing out of the heat source device on a basis of the outside air temperature and a temperature difference between chronologically preceding and following outside air temperatures, to thereby control the temperature of the subject to be controlled to be the target temperature, wherein the controller is configured to use, when executing the first control, a temperature difference between a temperature at a past time of the subject to be controlled and an outside air temperature of the past time, and a temperature difference between an inflow temperature at the past time and an outflow temperature at the past time of the heat medium that had flowed into and out of the heat source device, in addition to the outside air temperature and the temperature difference between the chronologically preceding and following outside air temperatures.