I drive a Peugeot 406 2.0 HDI, 2001. This morning it was -13 °C (9 °F) and the engine couldn't start. First two times, I could hear the engine running, but the third time it died and my temporary data was restarted (clock, date etc.). After I came from work, temperature was -4 °C (25 °F) and it started without any problems. I recharged the battery but it took very little time for complete charging. The battery is older than 10 years and the car was not used for a few months (up to 6). Is it just a battery problem or could it be something else?
Battery is probably the first thing to check, but given that it's a Diesel with cold start problems I would also get the glow plugs checked or check them yourself if it still has them.