A process fluid temperature estimation system comprising: a mounting assembly configured to mount the process fluid temperature estimation system to an external surface of a curved process fluid conduit ; a sensor capsule having an end configured to contact the external surface of the process fluid conduit , said sensor capsule having a relatively flat lower surface , to form an interface having a contact region and an air gap between the relatively flat lower surface and the curved process fluid conduit , the sensor capsule having at least one temperature sensitive element disposed therein; measurement circuitry coupled to the sensor capsule and configured to detect an electrical characteristic of the at least one temperature sensitive element that varies with temperature and provide at least process fluid conduit skin temperature information (T skin ); a controller coupled to the measurement circuitry , the controller being configured to: obtain the process fluid conduit skin temperature information (T skin ) from the measurement circuitry ; obtain reference temperature information (T reference ), obtain a heat flow parameter related to the air gap of the interface, and employ a heat transfer calculation with the process fluid conduit skin temperature information (T skin ), reference temperature information (T reference ), and heat flow parameter to generate an estimated process fluid temperature output. a mounting assembly configured to mount the process fluid temperature estimation system to an external surface of a curved process fluid conduit ; a sensor capsule having an end configured to contact the external surface of the process fluid conduit , said sensor capsule having a relatively flat lower surface , to form an interface having a contact region and an air gap between the relatively flat lower surface and the curved process fluid conduit , the sensor capsule having at least one temperature sensitive element disposed therein; measurement circuitry coupled to the sensor capsule and configured to detect an electrical characteristic of the at least one temperature sensitive element that varies with temperature and provide at least process fluid conduit skin temperature information (T skin ); a controller coupled to the measurement circuitry , the controller being configured to: obtain the process fluid conduit skin temperature information (T skin ) from the measurement circuitry ; obtain reference temperature information (T reference ), obtain a heat flow parameter related to the air gap of the interface, and employ a heat transfer calculation with the process fluid conduit skin temperature information (T skin ), reference temperature information (T reference ), and heat flow parameter to generate an estimated process fluid temperature output. obtain the process fluid conduit skin temperature information (T skin ) from the measurement circuitry ; obtain reference temperature information (T reference ), obtain a heat flow parameter related to the air gap of the interface, and employ a heat transfer calculation with the process fluid conduit skin temperature information (T skin ), reference temperature information (T reference ), and heat flow parameter to generate an estimated process fluid temperature output. <EOS>