The interior dynamics of a relativistic fluid in a shear-free spherically symmetric spacetime are investigated. The isotropic matter distribution is an imperfect fluid with a nonvanishing heat flux which is in the radial direction. The pressure isotropy condition is a second-order nonlinear ordinary differential equation with variable coefficients in the gravitational potentials. We impose a particular on these potentials and a new class of solutions are obtained, containing those of Bergmann and Modak. A physical analysis is then performed where the matter variables are graphically plotted and the energy conditions are shown to be satisfied. Causality is also shown not to be violated. An analysis of the temperature profiles indicates that closed form expressions can be generated for both the noncausal and causal cases.