DSLR chip overheating and max clip length
First, while sensor temperature is a real thing that can result in elevated noise levels, I'm not aware of a sensor in recent history that had a heat related shutdown (outside of harsh conditions anyway) or that could accumulate enough heat to be a threat to the chip.  Most of the non-sense out there about sensor's overheating is completely uninformed rumors or based on older sensors where heat was more of an issue.  There may be some exceptions in specific models, but they are not a major issue in runtimes or live view itself wouldn't work regardless of recording.  (Live view uses the sensor just as much or more than video recording does.)  There are three main factors that can limit record time.  

The first is card speed.  If you have a memory card which is not fast enough to sustain writing at the data rate of the video you are recording, the buffer of the camera will slowly fill and when it runs out of space, there is no way for the camera to continue recording.

The second is a limitation of the FAT file system used in many digital cameras.  Video files are very large and the FAT file system used in many cameras is simple and outdated.  It has a limit of 4GB per file and when you reach that limit, the file has to end or it will become unreadable.  In the case of your D5200, this is the reason for the 20 minute cut off.  Other cameras get around this either by using exFAT (a newer card format) or simply splitting the video between files.  (One file ends and a new file begins while the camera uses it's buffer to store frames.)  The later is, for example, how the Canon 5D Mark iii deals with 4GB file size limits.

The third and largest limitation is that of import taxes that the EU imposes on "video recording devices."  Video recording devices are defined as anything that can record more than 30 minutes of video and it is a 15% tax.  Thus, most manufacturers impose a completely artificial 29 minute 59 second time limit on video recording so that the device is not a video recording device.  Some manufacturers offer different versions in Europe than the rest of the world, but most just put the limit everywhere.

Third party firmwares are often able to deal with both the second and third situation (both by file splitting methods normally), however the first situation can only be addressed by getting a new, faster memory card.