DNA decomposition isn't a phenomenon that is too common. In _nearly all_ cases, DNA is broken apart to the accidental contamination with nucleases. Long-term storage of DNA in the -20 is also suggested in order to significantly lower the rates of these nuclease enzymes.
Additionally, DNA only truly fragments at very high temperatures (>90-100 degrees Celsius) due to the nature of the covalent chemical bonds that form DNA. Nearly any organic molecule will degrade at very high temperatures, and some will degrade at lower temperatures due to unstable structures or heat-labile bonds.
Of course DNA will deanneal at somewhat-high temperatures due to its double standedness , but allows for reannealing to the initial molecule once the temperature is brought down.
One additional reason for potential DNA degradation is DNA shearing, which will occurs when you tear up your DNA physically due to exposure to rigorous shaking, resuspending or other "violent" techniques.