  We extend an algorithm of Deng in spherically symmetric spacetimes to higher
dimensions. We show that it is possible to integrate the generalised condition
of pressure isotropy and generate exact solutions to the Einstein field
equations for a shear-free cosmological model with heat flow in higher
dimensions. Three new metrics are identified which contain results of four
dimensions as special cases. We show graphically that the matter variables are
well behaved and the speed of sound is causal.
