Hi, welcome to the group.
Strange these things should not happen, for the lead to heat up it
must be passing an appreciable amount of current.
Monitors and computers contains power supplies as we all know,
although they are usually 'switch mode' types, there is usually a
very small amount of leakage current passes from the mains or primary
side to low voltage or secondary side, this current is tightly
controlled by law and must not exceed certain factors - this is where
IMPAT testers comes into play that says if the equipment is safe to
use or not.
Consider this, a transformer can indeed become leaky, through an
internal flash-over or short, this would allow the primary mains
power to leak through to the secondary side, the equipment may
continue to function sometimes a ripple or hum can be seen or heard
on the monitor.
This larger than usual leakage current from the primary side will flow
through the supply line's of the secondary side putting everything at
that potential.... the circuit is completed when any other equipment
is connected that is grounded, this 'could be' one explanation.
It would be advisable to try a different monitor, or try a different
computer on that monitor - process of elimination, or indeed have
both units IMPAT tested.
The secondary side of computer equipment is usually grounded, the
earthing connection on both units NEEDS to be checked for your own
safety, if both units were at the same potential then the leakage
current however great will flow through the earth connection.. and
not through the casing, video lead and then to ground.
The power that these leads carry is very small, so small not to light
even a flashlight bulb - so if the lead is running warm
there is something dramatically and dangerously wrong that needs to be
seen to and sorted.
...
The fault could lay in either unit.
Davy