We numerically investigate the power and energy scaling potential of cryogenic Yb:YLF regenerative amplifiers in rod geometry. Our approach is based on solving the coupled set of equations describing thermal behavior of the material and its effect on spectroscopic properties, gain, and overall amplification. The approach is first benchmarked with earlier experimental data. By carefully analyzing the sensitivity of the system to operation parameters, we see that the relatively low gain nature of the Yb:YLF and the onset of thermal effects are the main factors that limited the performance in earlier experimental work. We show that usage of dual-rod geometry promises much improved performance. Specifically, we demonstrate that sub-250 fs pulses with an average power of up to 270 W and a peak power above 500 GW can be extracted directly from a single-stage Yb:YLF regenerative amplifier employing dual Yb:YLF rods. We further show that by adjusting the spot size in the regenerative amplifier, one can operate the amplifier in either high-energy mode (>100 mJ at 1 kHz) or high-average-power mode (>25 mJ at 10 kHz, with >250 W). We also discuss pros and cons of Yb:YLF with respect to Yb:YAG, and underline the need for measurement of population and photo-elastic-effect-induced lensing in Yb:YLF to obtain a better understanding of Yb:YLF systems. The findings presented in this work can be used for the design and development of next-generation high-average and peak-power Yb:YLF amplifier systems.