The rapid release of 5G wireless communications networks has spurred renewed concerns regarding the interactions of higher radiofrequency (RF) radiation with living species. We examine RF exposure and absorption in ex vivo bovine brain tissue and a brain simulating gel at three frequencies: 1.9 GHz, 4 GHz and 39 GHz that are relevant to current (4G), and upcoming (5G) spectra. We introduce a highly sensitive thermal method for the assessment of radiation exposure, and derive experimentally, accurate relations between the temperature rise (ΔT), specific absorption rate (SAR) and the incident power density (F), and tabulate the coefficients, ΔT/ΔF and Δ(SAR)/ΔF, as a function of frequency, depth and time. This new method provides both ΔT and SAR applicable to the frequency range below and above 6 GHz as shown at 1.9, 4 and 39 GHz, and demonstrates the most sensitive experimental assessment of brain tissue exposure to millimeter-wave radiation to date, with a detection limit of 1 mW. We examine the beam penetration, absorption and thermal diffusion at representative 4G and 5G frequencies and show that the RF heating increases rapidly with frequency due to decreasing RF source wavelength and increasing power density with the same incident power and exposure time. We also show the temperature effects of continuous wave, rapid pulse sequences and single pulses with varying pulse duration, and we employ electromagnetic modeling to map the field distributions in the tissue. Finally, using this new methodology, we measure the thermal diffusivity of ex vivo bovine brain tissue experimentally.