my %values= (
    '^' => '^',
);

...

s!\^\(([^)]+)\)!$values{ $1 }!g;

##</code><code>##

package My::Document;

*{"My::Document::^"}= sub { "^" };

sub name { $_[0]->{name} };

sub fill_template {
    my( $self, $template )= @_;
    $template=~ s!\^\(([^)]+)\)!$self->$1()!ge;
    $template
};

package main;
my $t= bless {
    name => 'wanna_code_perl',
} => My::Document;

print $t->fill_template(<<TMPL);
    Hello ^(name).
    Escaped: ^(^).
TMPL
;