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#!/usr/bin/env perl

...
    open my $out_fh, '>', $file_of_search_counts;
    print $out_fh "$_ : $count{$_}\n" for sort @search_terms;
}

$ cat file_to_search
100008020Z
...
100008040Z
Z100008040
100008040

$ cat file_of_search_terms
100008010
...
100008030
100008040
100008050

$ cat file_of_search_counts
100008010 : 0
...
100008030 : 2
100008040 : 2
100008050 : 0