The guys asks for help and he gets a lot of opinions.
So, from someone who actually uses these, works on them, installs them etc.
You can leave it plugged in as long as you want. If its been put on by the factory or dealer (mine was factory which I can verify, as the car was still wrapped up in the shipping warping when I first looked at car and the heater pad was listed on the details sheet).
The oil pan heaters are sized per the oil capacity (if done professionally, and the oil pad heater companies put out charts to do so yourself) ) so as not to burn oil. As its synthetic oil, you would have to have it pretty hot anyway.
I plug ours in (when used) when I got to bed at night, and 8-15 hours latter fire it up (weekends I sleep in). No issues.
Oil Pan Vs Circulating Heaters:
This is not a question. An oil pan heater is better for the engine. Period. Getting oil to the engine is the most critical aspect on startup. Worst wear takes place on startup up.
Having your oil at a temperature it flows and pumps better (quicker) to all the bearings is the most important. Circulating heater does not help any of that.
From a comfort standpoint, the circ heater works better. It also assist the fuel mileage situation by having the engine closer to optimum operating temperatures and helps craning. It also means you defrosters works quicker or right away and that also very important.
However, the oil pan heater left on overnight also warms the engine up some, as well as the tranny, which helps the whole situation.
Burning UP:
If you read the post on this, ANY electrical device can burn up. I have seen circulating heaters burn up as well. Be sure you have a working GFI (and or plugged into one). That will catch that sort of an issue.
My lady friend had her stove catch fire right after she bought the place, and it was professionally inspected.
If your GFI trips, fix the heater/circ heater immediately, do not plug it into a regular receptacle to keep it going. The GFI is telling you there is a problem (change cords just to check, though cord damage that causes that is usually obvious).
And, for those who question this, I have a special issue with a standby gen set that is very cold in winter at the bottom (oil pan) due to room setup. I have had the oil pan heater on it for 8 years. I take oil samples, The oil comes out clean (low hp version of the 5.9 so it does not crud up and I load bank it). Oil sample comes back in perfect condition
THIS IS ONE 24 HOURSS A DAY 365 DAYS A YEAR. I believe the VW is around 75 watts. So its like having a light bulb on all night. A circ heat is 1000 to 1500 watts. That is like 15+ light bulbs on. You can save money with the oil pan heat