Word on the street is to use your freezer and a pan of hot (±130°) water. Allow a 5 - 10 minute temp soak, then watch how it affects the plunger.
Don't expect "climate control" results. Be glad that you have the cap tube. I know of no place that replaces those that are missing, judging by forum posts.
When I dug into my heater control valve guts, I noticed that the plunger stroke is hardly enough to shut off the flow through the valve...and this is independent of the capillary tube.
Bill