Can fire cross walls into another room after an explosion?
Squares are not adjacent if there is a wall or closed door between them.  From Page 2 of the rules


  Any reference in the game to Adjacent spaces means those spaces that
  are up, down, left, or right from a space. Diagonal spaces are not
  Adjacent. Closed Doors and Walls prevent spaces from being Adjacent –
  unless the Wall segment is Destroyed. A Wall segment with two Damage
  Markers is Destroyed. A Wall segment with one damage marker is
  Damaged.


An open door or a destroyed wall (one with two damage counters) does not prevent adjacency.  So in each direction you will either find an adjacent space without fire (which you will add fire to) or run into a wall/door (doors are destroyed, walls are damaged) or reach outside (add fire but remove it at the end of the turn).