Heat death was the result of entropy in the universe increasing to the maximum amount possible to exist. When this occurred, all structure completely fell apart, leaving absolutely nothing behind, and further events could no longer happen.
Long ago, the universe passed the point into total collapse. The Logopolitans created CVEs into other universes to postpone the time until heat death occurred while their Advanced Research Team would formulate a more permanent solution. Due to interference caused by the Tremas Master in 1981 the CVEs closed prematurely, causing entropy to build up much faster than previously had. As entropy built up, it destroyed the Logopolitans, including the Monitor, and caused their planet to crumble to dust. The entropy quickly built up to the point of heat death which then spread through universe in the form of an entropy wave. The heat death caused by the wave destroyed planets and other astronomical objects in its path, reducing whatever part of the universe it reached to nothing. Heat death in N-Space occurred in places such as that of the Traken Union and much of the rest of the universe, resulting in the destruction of whatever was there. The Fourth Doctor prevented heat death from occurring across all of N-Space by redirecting this entropy into E-Space through a CVE in the constellation of Cassiopeia. (TV: Logopolis)