Pot size and nute burn

is it possible that a larger pot would cause an already hot soil to stay "too hot" for a longer period of time than a smaller pot with the same soil and being given the same amount of water?

No - really no need to worry about hot soil, many say for example Fox farms soil 's are hot - never found that true, even when using correct nutrient amounts - but if you feel your soil is "hot" just reduce your nutrient amounts. size of containers has nothing to do with hottness - large containers will give you a better yield. size of containers ? Generally if one states if soil is to hot ; it nutrient use. What type of soil are you using ? If really is to hot add top soil to your mixture

Ffof
Here's the thing though. FFoF comes with nutrients in the soil. That said, if I'm giving 2 plants the same amount of water, wouldn't it take longer for a plant in a ten gallon container to "use up" the soils nutes compared to what's in a 5 gallon bucket?

Yes