Perl et Variable

Mon probléme: 
J'ai un fichier de variable:var.txt 
$$DATE1=01/01/79 
$$DATE2=01/01/80 

Un fichier de parametre param.txt 
$$DATE1=05/05/05 
$$DATE2=06/06/06 

Comment remplacer les valeurs de param.txt par celle de var.txt? 
Je veux à la fin avoir dans param.txt: 
$$DATE1=01/01/79 
$$DATE2=01/01/80 
Je sais le faire en shell pour ceux que ça interesse: 

#! /usr/bin/perl

use warnings;
use strict;

open VAR,"var.txt" or die "E/S : $!\n";
open PARAM,"param.txt" or die "E/S : $!\n";
open RES,">resultat.txt" or die "E/S : $!\n";

my @p = <PARAM>;
my %h;

while (<VAR>){
  my ($x,$y) = $_ =~ /\$\$(.*)=(.*)/;
  $h{$x} = $y;
}

map {for my $e(keys %h){ if ($_ =~ /(.*)$e=?.*/){ $_=~ s/.*/\$\$$e=$h{$e}/}}} @p;
print RES @p;

[lamitest@localhost my_perl_script]$ cat var.txt
$$DATE1=01/01/79
$$DATE2=01/01/80
$$var100=10/10/10
$$VAR1=01/01/01979
$$VAR2=toto
$$VAR3=3
[lamitest@localhost my_perl_script]$

[lamitest@localhost my_perl_script]$ cat param.txt
$$DATE1=05/05/05
hfgh
$$DATE2=06/06/06
sdf
$$var100=ksdjfklj
yyyyy
$$var=OOOOO
$var4=titi
$VAR1=01/01/1970
[des autre variables]
$$VAR2=tonton
[du blabla]
$$VAR3=4

[lamitest@localhost my_perl_script]$ perl ccm_line.pl
[lamitest@localhost my_perl_script]$ cat resultat.txt
$$DATE1=01/01/79
hfgh
$$DATE2=01/01/80
sdf
$$var100=10/10/10
yyyyy
$$var=OOOOO
$var4=titi
$$VAR1=01/01/01979
[des autre variables]
$$VAR2=toto
[du blabla]
$$VAR3=3
[lamitest@localhost my_perl_script]$

rename 'resultat.txt','param.txt';

map {for my $e(keys %h){ if ($_ =~ /(.*)$e=?.*/){ $_=~ s/.*/\$\$$e=$h{$e}/}}} @p;

map {for my $e(keys %h){if (/(.*)$e=?.*/){s/.*/\$\$$e=$h{$e}/}}} @p;

map {
 for my $e(keys %h){
   if ($_ =~ /(.*)$e=?.*/){
     $_=~ s/.*/\$\$$e=$h{$e}/
   }
 }
} @p;

map {
 for my $e(keys %h){
   if (/(.*)$e=?.*/){
     s/.*/\$\$$e=$h{$e}/
   }
 }
} @p;