<p>I made a few successful prints since I got my CR-10 two weeks ago and I didn't run into any major trouble. The printer is new.</p>

<p>Today I set it to "preheat" mode while I was preparing the SD card with the settings being 210°C for the nozzle and 60°C for the bed. When I wanted to start the print I noticed that the temperature showed as "actual temperature" on the printer's screen showed 233°C and it was going up steadily while the "requested" temperature was still 210°C.</p>

<p>Thiking it might be a mis-manipulation on my part I powered it down for a few minutes (I got scared by the high-temp) and then powered it back on. I then immediately requested the print to start. The CR-10 heated up to the proper value, started printing and kept heating the nozzle. I stopped it at 217°C.</p>

<p>I looked for an answer on the internet but all I could find is people having trouble with the nozzle not heating at all ...</p>

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).