[oil pan 4]

We know the best way to warm up something like a tank of fluid is an immersion heater. That way the heat from the heating element only has one place to go. The stick on heaters need to be insulated on one side or the heat will conduct and radiate to the cool air instead of the fluid to be warmed.
To quickly warm up the oil in a vehicle I am going to use a stock GE 1500 watt heater element. These elements are about an inch longer than hardware store replacemens.
Also remember that hot water heater elements are designed to heat water and water plus glycol mixtures.
Engine block heaters and hot water heater elements are almost identical in construction, since they do the same thing.

This hot water heater element is almost too long to fit in the oil pan of my big block chevy with out touching the other side. But you want ad much surface area as possible, more about that later.

So you have major physical and chemical differences of the oil in the oil pan versus coolant in a metal engine block.
Which means you can't just run these hot water heater elements at full power in oil like with an engine block heater. If the oil comes in contact with a surface hotter than 200°C to 300°C it will scorch, produce acids and sludge and that's bad.
Will a hot water heater element in oil produce surface temperatures in excess of what it takes to scorch oil?
I'm not 100% convinced it will but let's not find out.

So to be safe I will need to more than cut the power in half.
Then you are only heating 5 or 6 quarts of oil, compared to the cooing system where you have few gallons of coolant and at least a few hundred pounds of iron or aluminum with a big surface area. So with a block heater you are not going to over heat anything.
In the oil pan you can fry the oil easy.
And and don't forget oil has about half the specific heat of the coolant, so it warms up twice as fast.

Then you have thermal shock, you could accidently send very hot oil into a cold engine block. Bad.

That means the oil temperature will need to be limited.

The standard 1500w heater element has about 9.5 ohms of resistance. I was thinking about rigging up 2 heating elements in series but that would make almost 400 watts come off each heating element. That would heat the oil up really fasted compared to the engine block heaters warming the coolant. It could work but I don't want to do it that way.

So the oil will need to be heated slowly compared to the coolant and have its maximum temperature limited.
If my oil pan holds 5 quarts of oil that would weigh about 8 pounds. 1btu will heat the oil 2°F. So let's say I want to bring the oil temperature up to a maximum temperature of 120°F, let's say the oil is starting at 0°F. We will just round it and say it 500btus to heat the 5 quarts of oil. For every 1,000w of heat put off by a heating element you get around 3,600btu/hr.
Let's say I turned down the power some and the heating element put off 1,000 watts, it would heat the oil in like 8 minutes and scorch the crap out of it.
Let's make the target temperature 1 hour.
So we want to get 500btu per hour out like a 5,400btu/hr heating element. To do that we want to turn down the power to about 140 watts. With a 9.5 ohm heating element, well the rest of the math isn't too hard to figure out.

But in the real world with real losses I have a feeling the oil will never get up to temperature when it's 0°F with the wind blowing. I'm trying to think what a 150 light bulb feels like in the blowing cold if the light bulbs surface area was the size of an oil pan. I just don't see it working real well, or coming up to temperature any time soon. I actually did this once, I painted an oil pan one winters night when it was about 20°F out side then to get the paint to dry I set the oil pan over top a 150 watt light bulb.

So I think my target wattage should be at least 150 watts to no more than 250 watts.
Which means I need to send between 36 and 48 volts to the heating element. My transformer tig puts off exactly between 36 and 48 volts and my varrac makes any voltage I want. So I have temporary power.
I'm thinking I gut and rewarp a microwave oven transformer for the desired voltage.

Then I need a thermostat to cut off the power at the desired temperature level. I have a whole collection of screw in and surface mount thermostats in that temperature range all I have to do is pick 1 or 2. Two if I want a backup.

Now all I have to do is cut a hole in the oil pan weld it up so it doesn't leak, where it is well below the oil level when down a quart or 2 and positioned so the heater element doesn't hit the oil pump or pickup or dip stick.

At the very least I think I found several very good reasons why oil pan heaters are very uncommon.