Translation:Yesterday the temperature was minus three degrees.
It also work perfectly if you say "yesterday temperature was minus three degrees", but it is not accepted. Yesterday's temperature implies using the genitive in english, I wonder if to reflect the use of the english genitive you need to use the genitive in Russian, which is температуры for temperature, can you use "вечера температуры .... in this phrase?
*Yesterday's temperature implies using the genitive in english, I wonder if to reflect the use of the english genitive you need to use the genitive in Russian, which is температуры for temperature, can you use "вечера температуры .... in this phrase?"
«вечера температуры» is wrong
The possessive case (yesterday's temperature) can be translated into Russian as an adjective — вчерашняя температура or (if you want genitive) температура вчерашнего дня.
I disagree. This is a language course for beginners, and as such, I think it is reasonable to expect the 'correct' English translation(s) to be as close to the Russian one as is possible both grammar-wise and vocabulary-wise without losing the meaning or producing a very unnatural English sentence.
"Yesterday the temperature was minus three degrees" does exactly that.
Missing out the word 'temperature', or putting in a possessive (yesterday's ...) produces a good English sentence, but not the one that you were asked to translate. Moreover, if you try to translate these alternative translations back into Russian at some later date, you are less likely to remember how the target Russian sentence was worded, whereas the perfectly good literal translation should help you to get it right straight away.
If this was a translation course, and for people who already have a good level of Russian, then I would very much encourage the use of alternative translations where the translator feels they are 'better', but that is a different skill altogether.