I’ve not replaced anything like that before.
However, I can suggest that the crucial diagnostic is detecting the short, which can be done with a standard multimeter.
If you wish to verify the damaged component by heat this needs to be done while the board is powered (potentially dangerous) or voltage injected which could be fiddly.
A temperature probe could also be used if you want to do that. Some people use their finger to detect the heat (only do this a low voltages!) Or squirt some non conductive solvent or equivalent and it will evaporate quicker in hot areas, similar to what is shown in the video.
The alternative is to make a guess at which component has failed, replace it and see what happens, this is a valid approach. Or replace eg. all capacitors connected at that point.
With capacitors it isn’t easy to know which replacement values would be ok, using one of the same type if others are in parallel could work.
This is a common failure mode of tantalum capacitors, so they would be a likely culprit.
It’s not a straightforward task by any means but it is possible.