You don't show us what Perl code you used to insert the degree sign into the database. Most likely this brings us back to your original thread, in which some questions to your code are still open.
My personal recommendation is to avoid Unicode / non-ascii in your source code and use the \N{} notation:
use charnames ':full';
my $fahrenheit = "\N{DEGREE SIGN}F";
# ... use $fahrenheit where you otherwise would type °F
The difference between SQLite Expert, Perl and the console output still comes out to that the strings you display with  are undecoded UTF-8 strings. This can have multiple causes, as discussed in SQLite returns funny characters.
If you have mixed string in your table, you will have to run an UPDATE SQL command to fix your database. But before you do that, make sure that your code is consistent.
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