Unless there are special rules for it, you can't actually cast heat metal on a robot.
Robots are creatures. If you read heat metal, the target is objects (held by creatures).
Even if you allowed them to target the robot, the robot should definitely be allowed a save against it, and even if it failed they would get apply any hardness against the damage dealt.
Considering it only deals 2d4 damage (average 5) it's probably not going to do much damage to the robot.
You can still target the Robots integrated weaponry with Heat Metal.
You will still have issues with getting past its hardness.
Unless you're using called shot rules, you can't target individual parts of a creature. Even then it's questionable about whether or not they count as separate objects from the creature.
I would say that RAW probably doesn't allow you to use heat metal on the robots weapons.
However, as a GM would probably ignore the targeting requirement and allow it to work against any robot that was metal.
Except the rules for the Robot type Integrated Weaponry explicitly says they can be targeted by effects that can target a held, manufactured weapon and gives the examples of the Magic Weapon spell or Sunder attacks.
Heat Metal would certainly qualify.
Ahh, good find but you should clarify further because it's not as simple as you present.
Under the robot subtype (which doesn't currently seem to appear on Paizo bestiary) it says:
Integrated Weaponry: A robot that has a technological weapon (such as a laser rifle or chain gun) built into its body treats such weapons as natural attacks and not manufactured weapons attacks, and cannot make iterative attacks with these weapons. Integrated weaponry can still be targeted by effects that target manufactured weapons (such as magic weapon spells or sunder attempts), but as a general rule cannot be harvested for use outside of the robot's body once the robot is destroyed. A robot is always proficient with its integrated weapons. Integrated ranged weapons do not provoke attacks of opportunity when fired in melee combat.
But integrated weapons are specific weapon that a robot might have.
For example, the Annhilator robot has 2 claws and 2 integrated chain guns. The chain guns could be targeted but the claws could not.
When you initially said integrated weaponry I wasn't thinking of it having it's own separate ability description and didn't know it had one since it's not on Paizo's website (it's much more difficult to use d20pfsrd at work with website blocked).
The main discrepancy we had here is me reading integrated weaponry as meaning a weapon integrated into the creature as opposed to an actual mechanical game term that I didn't know existed.
Regardless, since almost all robots have hardness 10 heat metal will do no damage.