Electrothermal propulsion aims to provide a balance to the high thrust of chemical engines and the high specific impulse of electric engines. Electrodeless electrothermal thrusters aim to overcome the typical electrode material limitations that current implementations suffer, by removing the exposed electrodes and using electromagnetic fields to heat the propellant. Radio-frequency inductively coupled plasma (RF ICP) thrusters have received limited research, but ICP torches are widely used in other industries where very high temperatures are frequently achieved. It is known that heat lost to the walls is a major limitation in the performance of these thrusters and the propellant injection style can have significant effects on this heat loss and plasma stabilisation. This work presents the validation of a 3D, steady, turbulent, pseudo-coupled electromagnetic (EM) and computational fluid dynamics (CFD) model of the thruster with heat transfer, which can be used to investigate different injection methods, coil and thruster geometries to optimise the device. It validates well against previous experimental data, capturing the stagnation temperature variation with flow rate and power within 4-25% error depending on conditions, as well as the plasma location and shape. The development of an experimental setup of an RF ICP thruster is also detailed. A maximum temperature of 1800 K is estimated, with a thrust, specific impulse and characteristic velocity of 50.4 mN, 128 s and 1000 m/s respectively at 1500 W input power and 40 mg/s of argon mass flow rate. Higher mass flow rates did not yield improved performance due to instability. It is expected that the temperature, and stability of higher flow rates, will be improved with optimised injection, and the performance will be further improved with nozzle optimisation and propellant choice.