This is not an easy one to solve, the firmware of the printer should be keeping the printer at a certain temperature depending on the temperature setting and the current value. If the firmware is not able to keep the temperature at the requested level, but goes beyond that level, that could be considered "strange". As it measures the temperature (and reports it on your display) it must know that it is over the limit and thus should not power the hotend.
In this process there are a few possible candidates for you to look at:
- Check for a faulty MOSFET (sort of an electronic switch) on your controller board (is it leaking current to the hotend?).
- Check and or update the current settings for the PID values (settings for the control loop of the hotend). The PID values control the overshoot of the temperature. E.g. is this is very large overshoot? When incorrectly configured the temperature can get higher, but normally should never increase to infinity, are you sure it keeps rising? The determination of the new values is called PID tuning. Important commands (that need to be send over a USB connected printer with a 3D printer terminal application like Repetier Host, OctoPrint or Pronterface):
- The M503 G-code command shows the current settings (somewhere in the heap of all settings).
- The M303 G-code command can determine the values.
- Reflash the firmware
- Replace the printer controller board
You could replace the thermistor and the heater cartridge (just to be sure, most definitely not the problem, but they are really cheap to replace). The thermistor works as it reports the temperature, and the heater element doesn't get powered by itself.
As suggested below the most likely candidate for your problem is the MOSFET. These are pretty easy to replace (depending on your board) or replaceable by an external MOSFET module (if you happen to have one lying around).