In this dissertation we present measurements of cross-magnetic-field heat transport in pure electron plasmas confined within a cylindrical Penning-Malmberg Trap. The measured heat transport is dominated by "long-range collisions", which are not included in classical transport theory. Most significantly, long-range collisions are observed to cause heat transport which is $\it{independent \ of \ the \ magnetic \ field}$, as opposed to classical theory which scales as $B^{-2}$. Modern theory predicts that long-range collisions are effective up to a Debye length, and thereby predicts transport rates which agree with the present measurements to within $50\%$.

Experimentally, the electron plasma temperature is obtained versus radius and time by a newly-developed technique which measures the charge which escapes past controlled end-trapping barriers. We describe the technique in detail including the data collection, analysis and calibration. The method is validated via several experiments of the temporal evolution of the radial temperature profile including heating due to asymmetry-induced radial expansion, cooling due to cyclotron radiation and heating due to separatrix-crossing dissipation. The temperature diagnostic is shown to be robust and capable of obtaining spatial temperature resolution on the order of the Debye length. The technique is applicable to a variety of nonneutral plasma traps enabling temperature diagnostics for previously inaccessible experiments.

From the measured density $n(r,t)$ and temperature $T(r,t)$ data, heat transport is analyzed as diffusion due to random particle collisions, convection due to bulk plasma flow, plus source terms consisting of Joule heating and cyclotron cooling. From these experiments we determine the cross-field thermal diffusivity, which we measure over a range of axial magnetic fields from $1 < B < 13$ kG; the measured diffusivity is compared with the predictions from the classical and modern transport theories. Classical theory considers collisions with collision impact parameters up to the cyclotron radius whereas modern theory considers long-range collisions with impact parameters up to the Debye length. Over the range of magnetic fields studied, the predicted transport rates from the modern theory are $10^3 -10^5$ times larger than transport rates predicted by classical theory. The measured diffusivity is within $50\%$ agreement with the modern theory prediction and the measurements verify the magnetic-field-independence of the heat transport.