Tunnel-ionized plasmas have been studied through experiments and particle simulations. Experimentally, x-ray measurements show that the plasma temperature is higher for a circularly polarized laser-produced plasma compared to when linear polarization is used. A higher parallel temperature than expected from the single-particle tunneling model was observed through Compton scattering fluctuation spectra. Simulations indicate that stochastic heating and the Weibel instability play an important role in plasma heating in all directions and isotropization.