Forse devi definire la variabile in tutti i casi, perchè in tutti i casi la usi.

Codice PHP:
<FORM name="2", method="post">
<INPUT type="submit", name="submit", value="Accendi il forno"></input>
</FORM>
<?php
if(isset($_POST['submit'])){
       
$door_closed=true;
       }else{
       
$door_closed=false;
       }

if(
$door_closed==true){
       echo 
"door_closed=true";
       }else{
       echo 
"door_closed=$door_closed";
       }