The "heat death" problem stems from the recognition of 19h century scientists that the laws of thermodynamics imply a "running down" of the universe, caused by the approach of all matter in it to approach the same temperature. When this happens, energy exchanges vital for life stop, and life ends. Theologians engaged in the area of "Natural Theology" seek to discover clues to God's nature from natural phenomena. The heat death (really a "cold death" in an expanding universe) is a serious concern for such theologians. In fact, anyone interested in life and philosophy should ponder the implications of the supposed heat death, and a number of serious physicists have addressed the issue in recent years. The most cited is Freeman Dyson's 1979 Reviews of Modern Physics paper, titled "Time Without End."
I was invited recently to give a talk to the "Non-Theist" group at Roanoke's Unitarian-Universalist church. (I should clarify that UU churches are accepting of non-theists as well as theists!) Following is a link to the text of the talk, in which I discuss the impact of the heat/cold death on traditional theism, "religious naturalism," and pantheism. I also talk about Dyson's paper and the fecund considerations of physicist Paul Davies, and biologists Stuart Kauffman and Ursula Goodenough.
The non-theists at Roanoke's UU church are a very intelligent group, and I expected the Q&A discussion to follow to be interesting. I was not disappointed. An audio download is also available here.