The behaviour of dense hydromagnetic plasmoids interacting with a non-uniform axially symmetric magnetic field has been calculated using a two-dimensional fully ionized two-temperature hydromagnetic model. A two-step second order finite difference scheme similar to the Lax-Wendroff method is used to integrate the equations. Comparisons are made with the plasmoid experiments of Azovskii et al. A good correlation is obtained for the density and induced magnetic field, although significant differences exist between computed and experimental electron temperatures. The computed results indicate that thermal conduction along field lines can be a dominant loss mechanism.