Ian Evans:
Firstly, your temperature adjustment for the resistance is incorrect: R(90°C) = R(20°C) × [1 + coeff × (90 - 20)]
Secondly, are you considering an a.c. or d.c. system; if a.c. then you need to take account of the skin and proximity effects which will further increase the conductor resistance.
Once you have the correct resistance you can calculate the losses from the conductor (joule losses). All this energy needs to be removed from the conductor to maintain the temperature and you need to take account of all the heat transfer. Your system would need to monitor the temperature because as soon as it gets above the required temperature the losses will increase and you will get thermal runaway. As your system is 1 km long it is likely that the cooling gas will not be a constant temperature over the full length, it will be flowing around a system where the input will be colder than the output. When considering cooling of a long conductor it is generally easier to think in terms of W/m (You are basically looking at a fluid dynamics problem to remove the W/m).
Other things to consider are costs resulting from probable reduced reliability and additional maintenance - it isn't just about the savings in terms of energy losses.
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