I'll offer you some corrections even if someone has already done that task for you. Sometimes it's helpful seeing how someone else would correct your writing.

The gGreat hotHeat Wave [Scrivere un titolo, si cappitalizzano le parole, la prima inclusa, tranne gli articoli e le preposizioni]

In these days Recently, in Italy, there is ahas been very hot weather! [Di solito uno scrittore di madrelingua inglese scriverebbe "We have had very hot weather!]
My town isn't toovery far from the sea and so it isn't usuallya very hot town generally, but by quitefor almost a month, there ishas been a so called ball of hotheat wave that make raised temperatures untilto 40°C at shadowin the shade.
I have never been a woman thatwho sweats very much, but in these days I'm sweating even beingwhen motionless!! It's Aalmost like if I had beendid jogging for an hour! [È meglio scrivere "almost as if" ma scrivere "almost like" è accettabile colloquialimente"]

The Great Hot

In these days in Italy there is a very hot weather! There has recently been very hot weather in Italy!
My town isn't too far from the sea and so it isn't a very hot town generally, but by quite for almost a month there has been a heat wave and temperatures have risen to is a so called ball of hot that make raise temperatures until 40°C  in the shade.at shadow.
I have never been a woman that sweats very much, but in these days lately I'm sweating even being when I am motionless!! Almost as if like if I had been did jogging for an hour!