I fixed it recently by replacing the hand piece with a Chinese YAXUN 936 50W 24V unit which can be had on Aliexpress for around $7 .
The element in my one finally gave up the ghost recently. The thermocouple went open-circuit.
I'm going to move to something more modern (work still in progress), but I'd like to keep the old station as a backup/spare, so decided to do what Bigfoot did. In my case the replacement handle was described as being for "YIHUA/WEP 24V 50W Machine". Heater measures at about 12 ohm at room temp, compared to about 11 ohm for the original. Unfortunate that the tips are different, but no big deal getting a whole new set.
The devil could be in the sensor, but at least it appears to be a thermocouple, not some sort of PTC.
The replacement works, and the meter reading matches what the dial is set to, but I found the temperatures to be a lot lower than I was used to. All I currently have to check the temperature is a thermocouple which has Teflon covered wires, supposedly OK only up to around 255C. With that I found that with the dial set to 300, the temp was only around 245.
I can't turn up any calibration info for this device. The service manual for the similar T-2000 gives some clues, but that one seems to have less adjustments (has fixed resistors either side of the temperature control VR2?). I bit the bullet and tried tweaking the opamp gain (VR1) to get temp around 250 with the dial set to 250, but it was then a bit out at lower temperature settings, eg 163 when dial set to the minimum 150. The offset adjustment was a bit out, but correcting that via VR3 (and re-adjusting VR1 for correct temp with dial at 250) resulted in a greater error at lower temps.
It is probably usable as it is, but has anybody else tried messing with the settings?
FWIW, I see an error in the helpful schematic posted by Seronday (reply #4 here).
That shows a 1M resistor from negative supply rail to non-inverting input of opamp (pin 2). This is wrong - this resistor, designated R3A on the PCB, actually goes from negative supply rail to junction of VR3 and the 10K resistor. The PCB allows for alternative of R3 to positive supply rail, so you can have negative or positive adjustments, but have to move the resistor.