We laser-cooled up to 106 9Be+ ions to ∼1 mK in a Penning-Malmberg trap and measured the ion temperature as a function of time after turning off the cooling laser. We observed a rapid heating of the ions when their temperature in a direction parallel to the magnetic field increased above 10 mK and show that this is due to the equilibration of a warm (few kelvins) impurity-ion cyclotron motion with the parallel motion of the 9Be+ ions. The observed equilibration is more than 14 orders of magnitude faster than predicted by theory that is valid in the absence of correlations, and is closely related to the enhancement of nuclear reactions in dense stellar interiors, first predicted over 50 years ago by Salpeter. Future experiments similar to the work described here can be used to model nuclear fusion in dense plasmas. Finally, we describe an attempt to use the measured heating rate of the 9Be+ ions to observe the latent heat of the predicted solid-liquid phase transition.