My 2002 intruder is not charging the battery

Double check your battery to be sure that you bought the right kind. Also double check the reg/rec. This device is what is primarily responsible for the charging being correct. Overcharging should fall squarely on the shoulders of the reg/rec. if you didn't already replace it with a brand new part I'd still think that was the problem. If you did replace it, I suppose it is possible for your alternator to be broken and producing an absurd amount of energy, but I doubt it.

Check battery cable corrosion, clean tight connections. Check fuses. Unplug and replug every connector you can find.

if you are losing the charge only when the temperature gets low I would say that it is the battery, especially if it is the original one as most batteries only last about 5 years.

Check for a bad ground. A bad ground will wreak havoc on your charging system and battery. If you find the source of bad ground, you might as well check it with the components that are on there now. The regulator is the component that would most likely have gone bad since it the rectifier were bad, you wouldn't get any DC voltage from the alternator.

Check the started, it could be 'dragging' and could need bushes replaced and a general service.

Hi and welcome to the site,

Initially, have the battery checked, externally charged and load tested.

Offhand, check & clean:

• battery terminals/connections;
• main fuse and holder.

Good luck and thank you for asking.

Tire pressure is 29 lbs for the front and 36 lbs for the rear

It is a simple matter to take the plastic cover off the battery located directly behind the front wheel on the lower frame and connect a charger. Better to charge at 2 amp rather than higher.

Check the voltage across the battery with the engine running - it should be greater than 13.5V. 
If less, then you have a failure in your charging system, either the stator and/or the Rectifier/Regulator. 
See this personally authored diagnostic guide on how to determine which part is defective. Also has a recommendation for excellent replacement as opposed to std OEM. 
http://www.triumphrat.net/speed-triple-forum/104504-charging-system-diagnostics-rectifier-regulator-upgrade.html