If everything is properly installed and undamaged, ordinary connections (junctions between wires, between wires and receptacles, between wires and switches) should produce very, very little heat and definitely not feel noticeably warm to the touch.
Two key things to check, both easy enough to confirm/deny by opening up the receptacle boxes:
Back stab connections
There are four types of connections commonly found:
- Wires hooked around screws
This is the old standard. Make sure the wires are hooked around in the direction of the screw (i.e., clockwise) so that tightening the screw doesn't push the wire away. Make sure the bare part of the wire is fully under the screw with no insulation under the screw.
These are single-use connections, normally designed for 14 AWG wire (but many circuits will have 12 AWG wire). They are fast and easy to install, but if (a) not inserted all the way, (b) not stripped properly, (c) removed and reinserted or (d) wrong size wire then they can result in bad connections = heat = fire.
These are the best! You insert the stripped wire straight (like back stab, so no making a hook = fast and easy) and screw down to hold the wire(s) in place. Yes, wire(s) - you can usually have one wire on each side of the screw, which is an extra benefit. But the receptacles cost a little more than the cheapest ones - you get what you pay for. The same receptacles that include screw-to-clamp are also usually better designed in other ways. Well worth the cost, IMHO.
- Permanently attached wires
This is most common on smart switches, dimmers, etc. Instead of attaching wires in the box directly to terminals on the device, you use a wire nut to connect those wires to the device wires.
Any connection can go bad if repeatedly stressed or poorly installed. But back stabs seem to be most vulnerable to problems.
Aluminum Wiring
As Harper (and others) make clear, aluminum wiring is not inherently bad. However, aluminum branch circuit wiring, especially 15A and 20A wiring, has a very bad reputation that is well-deserved. Due to different expansion rates and poor installation practices, aluminum wiring installed with 15A and 20A receptacles, switches, etc. is a well-known problem. It can often lead to bad connections = heat = fire...
So open up the problem receptacle boxes and see what you've got.
If you have aluminum wiring then replacement of the receptacles with CO/ALR receptacles is highly recommended. If you have aluminum wiring, you should check every connection in each affected circuit, even if it does not feel warm. Any devices not rated CO/ALR should be replaced with CO/ALR, or add copper pigtails with AL/CU connectors (a.k.a., purple wire nuts).
If you don't have aluminum wiring but you have back stab connections, at a minimum move the wires to screw terminals. If any receptacle shows signs of melting, burning or arcing, replace it with a good quality screw-to-clamp receptacle.
If you find receptacles that are using screw terminals, redo the connections to make sure they are really solid (this is what torque requirements are all about). Again, if any receptacle shows signs of melting, burning or arcing, replace it with a good quality screw-to-clamp receptacle.