For an ideal conductor, thermal resistance is 

The thermal resistance of the perfect conductor is zero.
A steady current in the perfect conductor will flow without losing energy to resistance.
Resistance is what induces heating in the conductors because the ideal conductor does not produce heat.
Because energy is not lost to heat, the current does not dissipate; it will continue continuously inside the perfect conductor until there is no potential difference.
A perfect conductor is an idealized substance of infinite electrical conductivity.