You can put this implied "есть" wherever you want: it would be awkward in any position here. It is implied in such sentences indeed, but more often missed. In "У меня есть температура" it is fine, in "У тебя есть температура сейчас?" even almost obligatory (it can be in any position). I don't know the formalized rule.
Сейчас is like на данный момент - at this specific time. Фильм начинается через 30 минут, давайте сейчас в кино поедем. The movie starts in thirty minutes, let's go to the movies now. Нам не понравился фильм, а теперь мы никогда не будем смотреть фильмы такого жанра. We didn't like the movie, and now we're never going to watch that genre again.
I've heard my Russian friend use this phrase to ask what the temperature was like where I was at the time like "what's the temperature over there where you are," but since this lesson is about the body and stuff, I was wondering if you'd also use this phrase to ask what someone's temperature was in like a medical sense, like if they had a fever or not. Would you use the same phrase for either one?
I was wondering if you'd also use this phrase to ask what someone's temperature was in like a medical sense
Yes, and that's most likely the meaning they had in mind when they wrote this sentence. In fact that's the first meaning that comes to mind when I read this sentence. Though this being a question about the weather is possible as well.