The increased core electron temperature produced by ICRF heating of TFTR, D-T neutral-beam-heated supershot plasmas is expected to extend the alpha-particle slowing down time and hence enhance the central alpha-particle pressure. In preparation for the TFTR D-T operational phase, which started in late 1993, a series of experiments were conducted on TFTR to explore the effect of ICRF heating on the performance and stability of low-recycling, deuterium supershot plasmas in the 3He minority heating regime. The coupling of up to 7.4 MW of 47 MHz ICRF power to full size (R approximately 2.62 m, a approximately 0.96 m), 3He minority, deuterium supershots heated with up to 30 MW of deuterium neutral beam injection has resulted in a significant increase in core electron temperature ( Delta Te=3-4 keV). Simulations of equivalent D-T supershots predict that such ICRF heating should result in approximately a 60% increase in the alpha-particle slowing down time and an enhancement of about 30% in the central alpha pressure. Future experiments to be conducted at ICRF powers up to 12.5 MW during the upcoming TFTR D-T campaign may result in even greater enhancements in core alpha parameters. This paper presents results from experiments performed at an axial toroidal magnetic field of about 4.8 T, where the minority resonance was within 0.1-0.15 m of the plasma core. Combined ICRF and neutral beam heating powers in these experiments reached TFTR record levels of over 37 MW, which allowed an exploration of the power loading limits on the carbon limiter tiles. The plasma current was operated at 1.85 and 2.2 MA and sawtooth suppression was observed at the higher plasma current.