Wires don't get hotter (higher temperature) with increased length, they get hotter with increased current. You're probably thinking of those warnings we get with appliances or tools, that have the wire gauge recommendation charts for extension cords. Household power is usually supplied at a fixed voltage to a more-or-less fixed load, and that's not the case for vehicle charging.
Wire has a resistance-per-foot factor, which is lower for larger wires and higher for smaller. If you start out with 350v at a source, 10' down the wire maybe you'd only see 348V; 20' down maybe 345V, and so on. The wire's resistance is converting power into heat. We don't want heat in the wire, we want the power at our load at the end of the wire, so we use a larger wire that has less resistance, so more power ends up at the load and less power gets turned into heat.
In the case of the Tesla car, both the supply voltage and the load is variable. If the car decides to ask for, say, 125 amperes maximum -- and the car does actually do that, that's the way DCFC works -- and if the Supercharger is capable at that moment of doing that -- the SCs have variable capability, based on a whole list of factors -- then the SC will set its output voltage to the battery pack voltage, the contactors in the car and in the SC close, and . . . nothing happens immediately. The voltage on both sides of the cable are the same, no flow. This is done deliberately, to lessen the wear on the contactors.
The SC then raises its output voltage on a ramp, while monitoring the current. It keeps pushing the delivery voltage higher until the agreed-upon maximum current is achieved.
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The SC "knows" the current-carrying capability of the cable, via installation configuration parameters. It therefore "knows" the maximum current capability it should deliver, and it won't push delivery voltage higher than what the measured maximum amperage is at any given moment. That changes, as the car's battery pack resistance changes: the pack's resistance goes up as it becomes more charged, so the SC has to push delivery voltage higher to achieve that maximum amperage.
What happens when you add an extension cord to the chain? More resistance. The car is communicating with the SC constantly, several messages per second, in effect telling the SC, "keep going, everything looks good here", or "time to slow down, the pack is almost full", and like that. But neither the car nor the SC knows about the extension cord, and neither cares about it.
If the extension cord is of equal wire gauge (is as large as) the SC's own charge cable, the effect is a little more voltage drop across the extension cord, and nothing else. Nothing gets hotter -- as long as the heat dissipation capability of the extension cable is the same as the SC's cable -- more on that below.
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The car and SC are communicating constantly. I don't know Tesla's protocol, but other DCFC protocols (CCS, CHAdeMO) will sometimes compare notes, eg the charger may say, "I'm sending 350v" and the car may reply "I'm receiving 345v", and if there's enough discrepancy, the charging session can be aborted due to a large enough mismatch of values. Various implementations of the "standards" means that, in the non-Telsa world, it can be possible for a mis-match of a certain magnitude of sent/received voltage to trigger a charge session abort on one manufacturer's charger, but not another. This means that in theory it would be possible in the non-Tesla world for a DCFC extension cable to work OK on one charger but not another. (I am working on a hobbiest level in the CCS world right now, and we run into this a lot: "I love standards, so many to choose from!")
Fortunately, this extension cable supplier only has to deal with testing a single manufacturer's charger: Tesla! So, if it works on one SC, it should work on them all.
I'd be curious to know the technical details of how this extension cable tells the SC to limit the max current to the extension cable's max (it's not a liquid-cooled cable, so I'd guess it can't deliver what a SC's liquid-cooled cable could, without overheating), but in the end I don't need that info, as long as it does it. But it's not the length of the cable that's a concern, as long as it can dissipate heat as well as the SC's cable can.
