<p>I'm about to build a <a href="https://toms3d.org/2017/02/23/building-cheapest-possible-prusa-i3-mk2/" rel="noreferrer">Prusa i3 dolly</a>. I am confused whether to use RAMPS 1.4 or 1.5 or 1.6.</p>

<p>What is the big difference? Is it only the MOSFETs and the poly-fuses? If that is the case, would it be advisable to upgrade a RAMPS 1.4 board (replacing the MOSFETs, connectors, and fuses)?</p>

This can come from several sources:
Hardware
The thermistor or its connections might be damaged, and the fault is only observable when the hotend is hot or moved to a certain area. Start by checking the wiring! You may be able to repair a bad connection easily, but depending what was broken, you may need to replace something. In some cases squishing a thermistor cartridge too much can destroy the internals, so a replacement is needed.
A mainboard failure is more likely to just show a static temperature, and a heater failure would show as maybe not getting past a certain point.
Firmware
If it had not worked before or you changed the firmware, the firmware should also be a suspect. The firmware can 'fail' when using the wrong thermistor type/table which can result in a very big offset or bad slope, resulting in wrong or unaccurate readings.