Let $T$ be a normal random variable that describes the temperature... Let $T$ be a normal random variable that describes the temperature in Rome on the 2nd of June. It is known that on this date the average temperature is equal to $µ_T = 20$ centigrade degrees and that $P (T ≤ 25) = 0.8212$. How can I calculate the variance of $T$?

From $P(T \leq 25)=0.8212$, you can find the $z$-score of $25$ (reverse-lookup in a $z$-score table).

The $z$-score of $25$ is also given by $z=\frac{25-\mu_T}{\sigma}$.

Set these two expressions for the $z$-score equal to each other and solve for $\sigma$. Finally, square it to get $\sigma^2$.