How about: "Kakaya u tebya temperatura teper'"? Does this other version of "now" work?
I could be wrong, I think that would imply contrast with another point in time; e.g. you'd use it if you were checking temperature every few minutes.
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.
теперь is like saying "from now on" or at least a significant amount of time. Maybe it would make sense in the sentence "I was sick with a fever for weeks but now my temperature is normal".
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.
Why do we use у here? To me, it seems like I am calling "you" and asking "Hey, what's the temperature at your place?"
У тебя = you have. Direct translation would be more like "at yours", "at your disposal" (locative+possessive prep. "у" and "тебя"="you" in Genitive).
so you are a scientist reading how hot lava is and your associate says "what is "your" temp now. Yep, I know ..... "bl**dy hot" But in this case I think "What temperature do you have now" would work and possibly even be a better term. Could a native speaker write how they, as the associate would say this please? So that next time, when I'm on the side of a volcano, measuring the temp of a lava flow, with a Russian associate, I know what they are saying. )))