Ha-hah, I forgot that this is a photo-reference kind of forum.
Why do I change motor oil when the bike/vehicle is warm? Because at the end of a trip, it concludes my 5,000 mile interval. I let the motor cool off a little while I change out of my riding gear and take a short rest. Then the motorbike is ready for the next day/ride.
The only thing I changed at 3,000 miles was my '81 KZ550, that thing liked to burn oil. As a side note, don't believe anyone if they tell you that a motor shouldn't burn oil. On a BMW web site, it's stated that it's not unusual for a motor to burn up to 1 quart every 1,000 miles. That doesn't mean that BMW motors burn that much oil, just a heads up that if a motor does, don't be alarmed (and yes, I've taken BMW on 1,000-mile trips).
Also, I'm not a follower of the "3-month" rule of thumb. If I put on only 2,000 miles in 3 months, I ain't changing the oil. The "just in case" and "cheap insurance" excuses make people feel good, so good for them. For some reason, their vehicles are more special than other peoples'
This is a bad example only because it's in metric, but in any case the manufacturer never suggests 3,000-miles or 3-months: