This is not a new question here and here, but the details make it differ.
My input log file looks like:
TEMP MON -=- Sat Aug 15 02:20:24 EEST 2020 -=-
Using core module Time::Piece in Perl:
Time::Piece
perl -MTime::Piece -pe 's/-=-\s+\K(.*)(?=\s+-=-)/convert($1)/e; sub convert { $s = $_[0]; $s =~ s/\s+EEST\s+/ /; $t = Time::Piece->strptime($s, "%a %b %d %T %Y"); $res = $t->strftime("%Y-%m-%d_%H:%M:%S"); "$res EEST" }' file