Hello,
Thank you for your feedback!
Here is what I found, after "printer heated, thermal runaway" happened again.
First of all, I've checked bed connection GND, VCC and thermistor, looks fine:

and its connection on board:

nothing looks damaged:

Here is GND, VCC power connection, which at first glance looks fine:

As you've noted, it is some wiring problem, but it is not clear. If I keep bed connection this way:

bed temperature on board shows incorrect value, which is 28-32 degrees just with turning on and preparing with bed, and if I will touch wires with hand this way:

It shows correct temperature increasing, but as soon as I release it, temperature number drops to minimal 28-32 degrees false value, what produces "printer heated, thermal runaway" error.
The blue "led1" indicator in the middle, between VCC and GND, behaves chaotic, sometime blinks with failure value, sometime vice-versa, or does nothing or keeps constant light.
Seems like during failure (minimal temperature value on the display) bed continuous increase temperature above the given value, what seems dangerous, I guess "thermal runway error" should appear each time in such situation, but it is not.
It looks like, the reason is clear, it is wire, but I can't figure out where this problem location actually is, because all sides looks fine, and thermistor under the bed also looks good without any physical damage.
Here is another unclear thing, the red VCC power wire melts, now I found that the exactly this wire with ground wire becomes very hot and produces smell, by this reason once it was different "heating failed, printer halted" error, instead "thermal runway error":

It is two manifestations of problem, but I can't say for sure, if touching of wire helps with hot VCC wire, just shows correct temperature value with touching, as shown in pictures above, and fails again if I release my hand. It is unclear why VCC wire is hot, I don’t see anything physically damaged, seems like it goes hot when heated, then wire temperature decreases, when bed keeps temperature.
Then I found physical damage point, which normally should produce short circuit, between VCC and ground wires directly where they are connected to terminal on the board, wires was fused to each other, you even can see it in this picture above, but also when I've looked closer, it was the contact between wires, caused by melting, so reason of melting is not contact itself, and what is a more confusing, there wasn't short circuit, when I saw metal on both wires separated from each other, which was clearly in contact. I was happy to think, that this was a reason of the problem, I've removed VCC and GND wires from terminal, cleaned damaged plastic, isolated it with heat shrink tube.
But wire still hot, melts, and temperature on display jumps from real to minimal value, and bed is overheated if minimal failure value keeps long time, so real temperature goes above the given for example if given 55, then after failure to minimal can be 61 or higher, or gives "thermal runaway" error. Touching with hand now works almost same way as it was before repairing of wires, given the fact that I've putted insulating tape on bed connector too, to fix it in position, but nothing helps, looks like it fails less, and touching with hand still shows correct temperature, but not all the time. So, something is damaged.
I've bought this Pulse XE about year ago from MH. I don't know about warranty or replacement parts, I still even don't know what exactly causes this failure, to replace something, but if I get you right if it is board, should be this one I guess Semoic 1PC DC 10-28V Mini-Rambo 1.3 Control Board Set Kit 3D Printer Part for Prusa MK2 and I'm not sure which thermistor with wire must be suitable, something like this one maybe Mmei 5pcs NTC 3950 100K Thermistor with 1 Meter Wiring and Female Pin Head for RepRap 3D Printer Extruder Heated Bed pre-wired or Hot End
Now I'm trying to figure out, how to remove bed from Pulse XE properly to check thermistor, then if problem with it, need to figure out, which type of thermistor should I use to replace. When I'm checking connector end of thermistor, it does not shows anything with 200k 20k with ohm on multimeter, when heated bed or just turned off printer, VCC and GND on the bed side and terminal shows 10.4 V, anyway, I'm not sure if this checking is correct, at least I have to check it with continuous test, but there is nothing on internet like assembly guide for this task. I guess I should remove glued garolite from bed, but it seems that after removal it loses its ability to adhere, maybe after heating the glue grabs surfaces again, but nevertheless I would like to have at least some guidance for further actions: first of all, identify the problem and know which details to use for replacement. Because, as I know changing the thermistor must be correct, suitable device, and I can't see guide for board replacement as well
Also I was thinking about disable the bed runaway temperature warning to finish my particular work, because I am stacked now at an extremely inopportune moment. But I am alarmed by the fact that when the temperature goes to minimum, and then received from thermistor again, it rises above the settings limit.
And now seems like bed temperature does not shows anything on the display, when bed goes hot it keeps on 25-27 degree, sounds like thermistor completely lost.
Last solution I found possible, maybe it will work for me in this situation, I want try to print Nylon X with 0 temperature for bed, maybe it will work, because I am fixing the raft for security with flat thermoplastic clamps, it’s quite possible that I will be able to fix the first layer for current print without bed temperature somehow. When I'm trying export such setting from MatterControl it says "Bed Leveling Temperature, data compensates for machine misalignment and bed distortion, and ensures good first layer adhesion", but I've exported same setting to SD card with 0 for bed temperature, and what can I say, if I don't have to expect any other failures with this setting, first layer adhesion is very good, and I can use clamp in addition