A cooktop appliance includes a user interface, a gas burner, and a temperature sensor. A manually adjustable primary control valve is coupled to the gas burner. A secondary control valve is connected in series between the manually adjustable primary control valve and the gas burner. A controller is in communication with the secondary control valve. The controller is configured to adjust the secondary control valve in response to a user-determined set temperature, a temperature measurement from the temperature sensor, and a determined position of the manually adjustable primary control valve.