I usually know the rules pretty well, but am a bit unsure about this.
[1] The temperature of the pots are not the same.
[2] The temperatures of the pots are not the same.
[3] The temperature of the pots is not the same.
I think it should be [1] as [2] doesn't sound proper. I suppose [3] could be proper, but it sounds the strangest.
Another reason I think it should be [1] is that [2] should refer to the situation in which there are multiple items in each of the prepositional objects
The potatoes in the pots were not cooked properly. <- there are multiple potatoes in each pot, where as there is only one temperature for each pot.
Singular or plural for same attribute of a set of nouns
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Re: Singular or plural for same attribute of a set of nouns
#2 is correct.