So, the problem is in fact of a hardware nature. By replacing RAMPS 1.4, the problem went away.
Arduino, firmware, G-code... everything is the same, only RAMPS was replaced.
I'm going to find a suitable MOSFET replacement.
Sounds like you have a short in your sensor or sensor circuitry. However, if this is the case the sensed temperature is higher than the actual hotend temperature. Does your hot end go cold when the sensed temperature takes off? A short could also show the hotend temperature going up at an unrealistically fast rate. This doesn't seem to be your case.