How outlets are wired
In typical house wiring, the electrician will basically run one cable from a breaker through all the electrical outlets in a room (or maybe a few rooms. Ideally it will be labeled, if you look in your circuit breaker panel.) If the breaker is rated for 20 amps of current, it means it will "trip" (disconnect the circuit) if more than 20 amps of current flows through its cable. From the breaker's perspective, plugging a bunch of devices on a powerstrip into one outlet, is exactly the same as plugging those devices into the various electrical outlets in the room.
The reason for the breaker is that, as your devices draw more current, the wires that carry the current will get warmer because of resistive heating. The electrician chooses a wire thickness and a breaker rating that will prevent the wires from getting dangerously hot.
Though to answer your question -- doubling the electrical current will actually square the heat generated in the wires. There's not much difference between putting two devices in one outlet, vs one device in each of two outlets though.
Power Strip ratings
Your power strip should advertise a current rating, usually 10A or 20A. This is based on the thickness of the wires that carry the current in it. In a typical modern house circuit, there is a 20A breaker, and the electrical outlets are designed so that the connection between the socket and the device plug can carry the full 20A. So, if your power strip is rated for 20A, then it won't overheat. (That's really the only rating that matter for the power strip.)
However, in that example, if your devices add up to more than 20A of current, you will sometimes trip the breaker. If your devices are tripping the breaker, it means you're in danger of wires overheating if the breaker ever fails. The main thing to keep in mind: if you have a breaker that trips sometimes, you should take devices off of that circuit (or, if one device causes the breaker to trip or gets really hot, repair that device. Sometimes one device will have a failure that makes it draw a huge amount of current.)
The reason that people sometimes warn about "too many devices on a power strip" is that, if you have that many large appliances (computers, kitchen appliances, etc) on one circuit, you're likely operating it close to the breaker's trip point. It's safe to ignore that warning if you're plugging in phone chargers, clocks, and other things that don't use much power.
The only other concern is, if that one outlet has bad wiring, or the socket is making a loose connection to the plug, such that it overheats, it will be worse if you send the full 20A through that one plug. That's an abnormal and very unlikely condition in modern houses though. (In old houses, of course, all of this is less certain. If something is getting hot, don't use it.)