According to the textbook by Lehninger [1], a majority of proteins denature when heated in excess of 50-60°C, and some denature if cooled under 10-15°C. As far as which treatment, heating or cooling, is most irreversible, the answer is which ever treatment destroys the primary structure of the protein. Normally that would be heating since if you heat a protein to a high enough temperature to decompose it, then that is an irreversible change. Surprisingly, treatments - usually chemical - that break the disulfide bonds and disrupt the hydrogen bonding of the protein's primary structure were shown by Christian Anfinsen (shared the 1972 Nobel prize in chemistry) to be, many times, completely reversible [2].
Of course, the rules about thermal treatments of proteins mentioned by Lehninger have many exceptions when you consider more complicated structures such as spores (resistant to heat, cold, and probably radiation), organisms that live in extreme environments, etc.
[1] Albert L. Lehninger; Biochemistry, The Molecular Basis of Cell Structure and Function; Worth Publishers, Inc.; 1970; p. 59.
[2] David Dressler, Huntington Potter; Discovering Enzymes; Scientific American Library; 1991; pp. 148-149.
Excessive temperatures may cause denaturation. This is often the case. denaturation may result due to other affects such as thermal radiation as discussed in the former answer.