Another way to straighten tube (or wire, etc) is to unwind as much as you can, fit one end in the vice, and pull the other. As you do this you will feel the metal 'give' as you get past the springiness. That should be enough – at the cost, of course, of 2cm at each end.
If you don't feel the 'give' it may be that the tensile strength is more than you can pull. Annealing will help – but this can be counter-productive if you need elasticity – eg when making a coil spring.
Oh, look, John Baron has just beaten me to it.
And you will improve conductivity between tube and cylinder with solder – soft or (even better) hard.
Cheers, Tim