Go buy yourself a cheap multimeter. Check the voltage of your resting battery. It should be at least 12.5 volts, preferably higher. Check the battery when cranking the engine. It should not drop below 10 volts. Check it again with the engine running. I would expect some where around 14.4 volts.
Those are ball park numbers and there are posts that are more exact with the regulator used on the F800gs.
If you are getting around 14.4 volts with the engine running, it is not your stator. If the voltage is in the 15 teens or higher, it is the regulator. Readings in the 13 teens with a partially charged battery, your stator is probably going. Voltage the same as your resting battery voltage, is a clue your stator is shot.
Big drops in voltage at the battery when cranking, usually means a battery short. Battery voltage drops below 12.5 after being fully charged indicate a bad battery.
Until I did some voltage checks, I would not rush out and buy something yet. Temps in the low 30's makes the initial start on my bike a slow affair.
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