What happens to opposing magnets over time?

[brassmonkey]

I have two Neodymium disc magnets, with poles top and bottom.

If I forced the opposing poles together, what would happen to the magnets over a long period of time? Would the magnetism dissipate? Would one magnet change polarity? Or would nothing happen?

[Teddio]

Neodymium magnets are magnetically "hard" and the magnetic domains are very difficult to shift. It is unlikely that opposing poles would cause the domains to randomise to any degree so the magnetic flux density of the individual magnets wouldn't change.
Strong magnets have their magnetic domains lined-up parallel. Shock and high temperature will randomise the domains so there is no net direction. This results in the magnetism being "destroyed".

[Teddio]

The Earth's metallic core has a temperature of approximately 5000 Celsius. The Earth's magnetism is caused by electric currents circulating in the core.