Right, singular; there is no big difference between "each" and "every" in this case. Once you choose "s", it's to be "are" the same (the second sentence). People just don't care trivial stuff like this sometimes, it's not grammatically unacceptable, but logically. Like saying "heads of every one are connected to their necks", "everyone has his/her/their own problems", could be ambiguous: Could mean "each place has more than one temperature".