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Whether you use a shallow pan filled halfway with oil, a stovetop pot filled with oil or a deep frier, for the most part it is recommended that the oil is brought up to the same temperature (different for different foods, methods, oil mediums), but generally speaking betwee 345F–375F.
Clearly it will take longer to come up to that temp given larger amounts of room temperature oil, and materials of construction of pan/pot/frier, and dropping the food into the hot oil will result in different drops in temperature for similar reasons. Techinque (method, quantities, time, etc.) should be adjusted to compensate for these differences.
I think that's what you're asking?