|Agree that a poor connection at the "hot" end could/would cause the connector at that end to "get a little warm"...|
If the cable was starting to fail mechanically at the "hot" end - i.e. the inners were starting to fray/break... then that too could cause "heating up". On many an Apple adapter the cables fail at the laptop end of the cable (the plug that goes into the laptop) - but that doesn't "usually" get overly warm
If it fails in similar matter on the mains side close the mains plug or the adapter end ... then warming effect could/would be likely...
Many mains adapter/charger cables fail very close to the actual plugs on them; rather than somewhere in between. I have had to reject/replace few (cables) in the past for laptops that were (shall we say) subject to heavy (ab)use by the end users in a broadcast studio environment.
That it's the power cord (#3) would likely remove the warming effect from the laptop vents? But it doesn't totally eliminate the charger module being a little upset internally; nor a possible cable failure developing at the charger end; nor a dodgy/loose/intermittent connection there from the main power cord.
A few branded adapters do run "a little warm"; and certainly some of the third-party replacements do. Acer branded usually are OK; but some of the alleged genuine/guaranteed OK for Acer replacements (third-party) do run "warm". Similarly with Dell.
If it was the actual computer end of the cable getting warm... then it might be due to an incorrect size connector; and the difference is sometimes only 0.5mm between the correct one and one that "allegedly" fits... A family member had one such situation a while back with an alleged Acer compatible adapter. When he replaced the alleged "compatible" module with another (badged by Acer in this case) all was well; things no longer seemed a "a little warm there" - and the plug fit was also more positive...