In America we use the word "fever" instead of "temperature" when talking about health
I'm also American, and I was surprised to see your comment. I wonder if this depends on where you live, like "soda" vs. "pop." I and most people I know would say either "do you have a temperature" or "do you have a fever." They both are equally common where I'm from. I can't imagine asking "do you have a high temperature?" though. That is strange.
Some Americans actually say this. "Fever" is probably more commonly used these days, though.
This sentence reminded me my childhood. Basically, everybody has a temperature, except for a dead body out in the freezing weather. This is one of those sentences we made fun at as children. One child would ask another one, "У вас есть є температура?" The other child would say "No" and drop down, pretending to be dead and having no temperature at all. The right question about somebody's health would be if their temperature is normal, above normal or under normal. The translation "Do you have a high temperature?" makes sense to me but the Ukrainian sentence presented here sounds funny. Exactly because every body has some temperature, except for in the case described above.
Yeah, that English translation is incorrect. In English you'd say. 'Do you have fever? '
Interesting. Are you from the UK? Your translation sounds strange to me (American). I would always use the article: "do you have a fever?" To me, the only odd thing in the given translation is the word "high."