Multi-grade motor oil is measured in two weights, which correspond to cold (starting temperature) and operating temperature. Oil will have high viscosity when cold and a low viscosity at the engine's operating temperature. So basically your oil will have the viscosity of the first number when cold and the viscosity of second number when hot.
I'll use 5W30 as an example:
5W corresponds to cold start temperature - If you live in the north pole, you'd want to drop down the first number to let's say 0W-30 to account for colder starts. Conversely, if you live in warmer climates such as in your situation, you can raise this number because in Jacksonville you're not dealing with winter and cold starts. 10W would work fine.
30 corresponds to the viscosity of the oil at operating temperature. I personally
would not put oil in our cars that has a rating higher than 30. Here's why:
Our engine's ideal operating temperature is determined at the factory and then moderated by our car's cooling systems to prevent overheating. Let's say that this ideal temperature is 210 degrees. Irregardless if it's 30 degrees or 100 degrees outside, our car's cooling system is going to keep the operating temperature very close to 210 to prevent overheating and the engine from going kaboom.
I believe the owner's manual recommends 5W30 or 10W30 oil, meaning that at ideal operating temperature (or when the engine is hot) the viscosity of the oil needs to be 30. So again for example's sake, let's say the thickness of 5W30 oil at operating temperature is like water. 5W40 at the same operating temperature will be thicker - again for example's sake let's say maple syrup. Although it's an extreme example, the 5W40 oil will be thicker and won't be able move through the oil system as quickly, which could cause engine buildup and sludge. It will also be counter-productive as far as cooling is concerned, because it will take longer for it to flow through the engine.
However if your engine is burning oil at an excessive rate, then this can sometimes be addressed by using a thicker oil, a 10W-40 might not burn off as fast compared to a 10W-30. This is true for oil marketed as "High-Mileage" oil, as they tend to be slightly thicker for their grades and contain extra additives and seal conditioners. Being that your car has 20K on it, there is no need for a thicker viscosity as it shouldn't be burning much oil.
So what does all of this mean?
I would only use 5W30 or 10W30 oil for our cars. 10W30 being used in warmer climates where the starting temperature will never be something of that in Michigan in February. 5W40 will be too thick and has the possibility of creating sludge in your engine and could also void the factory warranty if you have problems. For your specific location in Jacksonville, 10W30 would work just fine.
