Here's the setup, going through those four valves will be some fluid, probably water, but I need some fishing line going through this cylinder to be sealed. The line is anchored at two points, the top and bottom, and will be used to draw two points together. This apparatus is to heat and cool wound up fishing line, as that can be used as a muscle fiber. When hot water is applied, it contracts, when cool water is applied, it expands. This does mean that the line will be moving some percentage of the length, which may also mean that the diameter will change slightly.
A high-quality seal that diameter would be very difficult to fabricate. You always want to avoid seals in designs when you can help it. For example, you could fix one end inside the cylinder so that you only have one moving end to worry about.
If you allow for some leakage and run the water at low pressure (less than 12" of head) you could probably get away with melting a small cup of wax around the line. Have the wax be as tall as the diameter of your primary tube. The longer distance will reduce water leakage. Pull the line taught while it cools so the path is straight. It should pull free with very little force, and with little movement during operation, it should provide a fair amount of operating life.
A more robust solution would be to put a diaphragm (as mentioned in the comments) on the end cap instead of a seal. The diaphragm will act like a soft spring, and can be compensated for with other spring components if necessary.
A design that you may or may not have considered; would be to use a single tube as your tension member and run hot and cold fluid through this tube. The design would be simpler, the volume of fluid per tension force would be lower, and the heat transfer would be quicker. Something to think about.