We use 'гарячо' for 'hot'. And yes, 'кішка' is a Russian word for 'cat'... I was always taught 'кітка' for a female cat and 'кіт' for s male cat. But never 'кішка'.
There was this crazy song called 'Who Stole the Kishka'...but it was supposed to be 'Who Stole the KYSHKA'...(Someone was hungry...LOL).
Russian and Ukrainian share lots of words because they are both East Slavic languages. There's nothing particularly wrong with жарко: http://sum.in.ua/s/zharko
Of course, «спекотно» should also be accepted.
It is so on the paper, but unfortunately, the essay with this word would get "F" (болезненный опыт с руссизмами и суржиком в научных статьях). It is just a bit awkward for a native speaker to see, that Duo teaches southeastern dialect of the country and doesn't consider "гаряче", "спекотно", "задушливо" as variants, however, they are much more common. Is there any accompanying program, that would help a non-Ukrainian speaker guess which word to use, if for example suddenly блакитний appeared to be substituted by "синій" курка - "кура", бордюр - "порєбрік", най- - "самий" черевик - "бачмага", малюнок - "кунст", життя - "живот" etc. without any alternative or explanation? I am asking only because of my research in "Digital study tools" - Duo is great anyway :)
I don't think there's an accompanying program for Duolingo for teaching more precise word differences. Comments and sentence notes are the best we have.
In fact, I haven't seen any accompanying programs for Duolingo. It would be nice to have some external infrastructure, but Duolingo is a pretty closed system that doesn't play well with the outside world. The programs I've seen just unlock some hidden features (such as 'word list'), that already exist in Duolingo but are hidden. I haven't seen a program that actually adds something to the course.
As for words, I agree that they should be accepted, and that жарко shouldn't be the default word. I've been over-reacting to "this is not Ukrainian but Russian" recently, because we have a person who goes as far as to claim that кішка is not a Ukrainian but a Russian word. But I definitely agree that спекотно sounds better.