They would get less hot, because there are plenty of transmission losses too.
When the charged stored inside a chip needs to change (like go from high to low), that energy associated with the charge needs to go somewhere. Currently most of the charge is dissipated in the wire and some of it within the transistor.
If the wires have no resistance, the transistor will be the one dissipating the energy, not the energy simply disappears.
So technically both options are right, but my position is the “technically right, but practically wrong” position lol
That said if the interconnects are less resistive, the switching process becomes more efficient and less power will be wasted than the bare minimum required.
If you have two capacitors, say C1 and C2, and say their capacitance is both C.
Say C1 is charged up to 2V. The energy stored in that cap is 1/2 CV^2 = 2C.
Say C2 is not charged up.
The charge on C1 is Q = CV = 2C. The charge on C2 is 0.
Say suddenly you connect C1 to C2 via a lossless wire.
The charge on C1 and C2 must be equal before and after the connection since charge cannot be destroyed.
After the connection, the voltage on both caps will be equal, and the charge on them will therefore be equal.
Charge on each cap is 1C; voltage is therefore Q/C = V, V = 1V on both caps..
Now let's look at the energy on either cap. 1/2 CV^2 = 0.5C.
The combined energy on both caps are 1C. Where'd the energy go? We just said we connected the capacitors with a lossless wire, so it can't be dissipated there, and capacitors by definition cannot dissipate power.
The answer is that lossless wires cannot exist, and if you do the math more carefully, this time with real resistance and take the limit as R->0, you will see that the power-time integral of the wire (dissipated energy) will approach 1C.
The same argument can be made for integrated circuits; as your resistance drops, more and more of the portion of loss will be dissipated in the "other" sources of loss.
edit: superconductors are lossy at AC (but not as much as regular conductors get lossy at AC), and the capacitor connection is an AC phenomena so even with superconductors there will be a teeny loss even with superconducting wires. The rest of the loss will happen in other ways (EM radiation, dielectric loss, loss from capacitor resistance, etc)
I vaguely remember switching current and leakage current as sources of heat, but mircoelectronic circuits has been a while for me...
RTP superconductors still aren't going to magically make computers emit zero heat, though; there are other sources besides resistive losses. I was under the impression that other factors dominated, though a couple people responded yesterday to tell me that resistance is the primary source of heat. Not an expert in that area, would love for someone who does chipset design to clarify.
There's many vast amounts of electricity wasted due to transmission losses. Magnets for fusion plants would become much cheaper.
Essentially, (and very top level) you could produce 30% more power, without adding any more production capactity.
But if that can be solved, then yes, it could make computing way more efficient.
Both of those go to zero. We may see 100ghz CPUs and 3D stacked cpus with almost no need for cooling.
If true, this specific case is only low current, but demonstrates such a thing is possible - almost certainly winning an instant Nobel Prize.