Can someone explain why this is happening?
 

When I first start my car ('82SC) in the morning, it has power and pulls like it's possessed, but after it gets warm it seems to lose that pulling power. I bought the car a month or so ago, and I've been planning to do a valve adjustment soon, could that be it?

I'd suspect your WUR is out of spec. Sounds like it may be going lean when warm. What temps are you seeing when the engine is hot? I'd throw some gauges on and check your cold and hot pressures. Do a search on checking pressures and you'll find plenty of threads on how to do this.

Temps tend to vary but generally they are between the second and third white bar. Can the WUR be adjusted or is it a replace item only?

WURs can be adjusted, rebuilt, or replaced. If you search WUR and my name you will see a recent thread in which I went through the WUR scenario.

You need to first verify that it is your WUR. You can do that w/ a fuel pressure gauge.