In the past I have landed overweight with the 737. Reason was uncontrollable hot air coming from both packs (70c/50c) on a hot summer day. I tried to go high first to cool them down unsuccessfully. Was about 8 tons overweight on landing, used the whole (long) runway, no autobrake, flaps 30, full reverse used brakes only to exit.
The heat was so intense I had to open the cockpit door and keep it open while descending. When at low altitude I even turned left pack off. Brake cooling was checked for the landing weight, no issues if brakes applied blo 100 kts.
Of course the fleet chief pilot had to ask why I landed overweight, I replied I could not hold and wait for the first passenger to die or the avionics to fail to declare an emergency. I changed aircraft and continued. The inspection was done, I was flying the same aircraft the next day. Cabin sensor problem.
It really helps if the company supports a "captain's discretion" decision.