I was thinking rather, put it in an ellastic tube and pass warm/cool liquid or air through it.

Pumping electrons vs. pumping (and heating) a fluid? There's a reason we don't use steam engines anymore :)

There's also a reason why we don't use Peltier pumps in refrigerators. Electrons are great at heating things, not so great at cooling them off.

In this case, that would mean that it would be fast to contract but slow to release. Our muscles have a similar problem, though maybe not quite as bad.

This is part of the reason our muscles work in antagonistic pairs, e.g. the biceps and triceps, where a joint moves based on the relative tension of the flexor and extensor muscles.

You would probably want to do a similar arrangement with these coils.

Yeah, but should probably point out the relative time scales involved. In muscle, once the nerve impulse is off, in a non-pathological state, muscle tension in the motor unit will drop to zero within hundreds of ms. For example http://www.bem.fi/book/21/fi/2108.gif shows a typical force-time curve for an impulse.

I have no idea what the equivalent would look like in this case, but I imagine in a purely passive cooling solution, it'd have quite a long time constant.

I don't have the paper, and in the abstract they awkwardly compare the strength to human muscle length and weight, when typically, its muscle cross section that bounds a particular muscles strength. This is important because if you start stacking these fibers in parallel to get more strength, then you pretty much dictate some sort of active cooling system to maintain any type of performance and control.

But not a good reason. Originally it was the boiler time-to-steam; but with a coil that's subsecond. We should really be using steam for lots of things.

Wire with current is awesome at warming stuff. Not so good at cooling. By redirecting the fluid or gas from warm and cool reservoires you could rapidly warm/cool the muscle. Even with whole bunch of muscles.

or melt it