Yes, warming the engine up makes the oil more liquid (viscous) and easier to pump
out. You may have other problems though if there is not enough oil to pump
out from the dip stick hole - even if the oil is cold it just moves slower through the pump
. I also use a 12V Jabsco oil pump
and even cold oil will get sucked out.
You should carefully check your oil dipstick to see what level the oil is at. The easy way to check the oil level is to take a clean paper towel or rag and wipe the dipstick down, then re-insert it and pull it out. Lay it up against the clean paper towel or rag and you will be able to see at what level the oil registers on the stick by the stain on the towel or cloth.
If you are just low on oil I'd advise getting a few quarts of cheap oil to put in and then run the engine for a bit and then pump out what you can. Check the color of the oil; dark is not good and milky is even worse. Dark oil just means that the crank case is dirty and needs a few oil changes to clean it out. Milky colored oil indicates that water has gotten into your crankcase; the cure for this is also several (3) subsequent oil changes to get most of the watery oil out of the engine. Also running the engine until it gets up to temperature after the oil changes helps get the remaining water out.
These old engines like fresh oil (change every 50 - 100 hours of use).
Use a good oil like Rotella T 30W oil to fill the engine after you have used cheaper oil to flush out the muck and/or water.
Good oil is cheap insurance.