Correct, hence the need for the probe to unroll the cable as it goes down. If you had the roll on the surface, you would need to heat the whole cable to allow it to slip down.
Back of the envelope feasibility check: assume the cable is a cylinder with diameter = 1cm, length = 25km. The area of the cylinder face is A = 2*pi*r*h = 785.4 m^2. The thermal conductivity of water ice is approx. 2.3 W / (m K). So to maintain a temperature difference of 10 K with the ice, you need 2.3 W/mK * 785 * 10 = approximately 18kW.
A mini nuclear-reactor-as-a-heat-source might be appropriate for a melt-drill. RTGs are a bit unfortunate as they'll exponentially decay from the time of manufacturing, and you'll need to both 1. deliver high enough power at Europa, and 2. radiate away that much power and a bit more when you're flying there.
A nuclear reactor could produce basically no heat while offline, then be switched on and suddenly provide 100s of kW when it gets to wherever it's going. The hard part in space is radiating away the heat, but if you're on an ice world, that's orders of magnitude easier.
The hardest part I'd see would just be getting into the ice; there's not really any "melting" in vacuum. The constant boiling away of the water would keep insulating your heater from the ice. Meters 1 to 20,000 are probably pretty easy.
https://www.walmart.com/c/kp/water-wiggler-toy
So it can "slip down" by a continuous unrolling process!