I see the fan and heater housing are all steel construction and I'm not supposed to really offer any safety advice here, there is a risk when making any changes.
The heater is high power at 1,500W which is not easily reduced. Capacitive droppers are practical for a few watts only. Probably easier to increase airflow.
The
Microtemp G4 TCO is rated for 15A/120VAC or 10A/250VAC.
You could consider the G5 series TCO which is rated for higher current, is the same size, and tolerates higher overshoot temps 225°C vs 150°C for the G4 110°C part.
The TCO might be too close to the resistance heating wire.
I would get a replacement TCO, solder it in at the rivets- but located farther away from the heating element.
Poke the leads through the rivet holes and with heatsinking on the TCO leads, solder it. This is very difficult- to not wreck the TCO from the heat.
Otherwise you need crimp ferrules and somehow to get in there with the tool, it's cramped.
NTE includes ferrules.
It looks like ordinary PVC wire/heatshrink tubing for the wires going to the connector. This means around 105°C is the material (plastic) limit. You can look at the wires to see if they are truly running too hot or something else is causing the TCO to fail.
It can also be the shutdown process - it should turn the heater off yet run the fan for a few seconds to cool off the heater.