Nemesis: Retaliation · Board game rules
Can a Robot move through a Room on fire?
Quick answer
Yes — the Robot can move through or into a Room with Fire; Fire only damages Characters and Intruders, not the Robot.
Details
Robot movement rules state that "The Robot always moves from a Room to a neighboring Room. It ignores Intruders (even the ones in Corridors), but it cannot move through Closed Doors" [p.37 — ROBOT]. There is no mention of Fire restricting the Robot's movement.
Fire markers are explicitly described as affecting Characters (who lose 1 Health Point if they end their Turn in a Room with Fire) and Intruders (who take 1 Hit during the Intruder Phase) [p.23 — MAP MARKERS AND TOKENS]. Since the Robot is neither a Character nor an Intruder, these Fire effects do not apply to it.
Watch out: while the Robot itself is unaffected by Fire, it still cannot move through Closed Doors or Explore new Rooms via Unexplored Corridors (with the sole exception of the Exploration Robot effect) [p.37 — ROBOT].