This work presents the development of a novel and non-invasive method that measures fluid flow rate and temperature in pipes. While current non-invasive flow meters are able to measure pipe flow rate, they cannot simultaneously measure the internal temperature of the fluid flow, which limits their widespread application. Moreover, devices that are able to determine flow temperature are primarily intrusive and require constant maintenance, which can shut down operation, resulting in downtime and economic loss. Consequently, non-invasive flow rate and temperature measurement systems are becoming increasingly attractive for a variety of operations, including for use in leak detection, energy metering, energy optimization, and oil and gas production, to name a few. In this work, a new solution method and parameter estimation scheme are developed and deployed to non-invasively determine fluid flow rate and temperature in a pipe. This new method is utilized in conjunction with a sensor-based apparatus--"namely, the Combined Heat Flux and Temperature Sensor (CHFT+), which employs simultaneous heat flux and temperature measurements for non-invasive thermal interrogation (NITI). In this work, the CHFT+ sensor embodiment is referred to as the British Thermal Unit (BTU) Meter. The fluid's flow rate and temperature are determined by estimating the fluid's convection heat transfer coefficient and the sensor-pipe thermal contact resistance. The new solution method and parameter estimation scheme were validated using both simulated and experimental data. The experimental data was validated for accuracy using a commercially available FR1118P10 Inline Flowmeter by Sotera Systems (Fort Wayne, IN) and a ThermaGate sensor by ThermaSENSE Corp. (Roanoke, VA). This study's experimental results displayed excellent agreement with values estimated from the aforementioned methods. Once tested in conjunction with the non-invasive BTU Meter, the proposed solution and parameter estimation scheme displayed an excellent level of validity and reliability in the results. Given the proposed BTU Meter's non-invasive design and experimental results, the developed solution and parameter estimation scheme shows promise for use in a variety of different residential, commercial, and industrial applications. / MS