random thoughts about training

Cadence: Those who advocate high cadence do so with the understanding that it WILL raise your heart rate. What they claim, roughly, is that the higher cadence trades intensity of work for the leg muscles (per revolution) for higher cardio-vascular stress. If your cardiovascular system can handle the stress then, the theory goes, the tradeoff is worth it.

So presumably there is a happy medium between mashing and spinning out that is the point at which you have hit the correct balance between intensity of work of the leg muscles and stress on the cardio-vascular system. I'm guessing that the best way to find this point is to understand what you are looking for, then experiment.  It will of course depend on leg strength and the capacity of your cardio-vascular system.  (Armstrong has amazing cardio-vascular capacity, but not huge legs (relative to some other cyclists), which is why, I'd guess, it makes sense for him to spin fast.)

Running: Hard to say. Of course warming up generally makes running easier. I don't normally start feeling good in a marathon until around mile 5 or 6. But I guess without more info it's hard to say what is going on in your particular case. My guess is: you are biking with sufficiently low intensity that when you are done, your body is well warmed up (heart pumping, oxygen being delivered efficiently, fuel being burned efficiently), so that you are ready to run, but not biking so hard that you are dead for the run.

It doesn't always work that way. On one of my first few bricks, I went out way too hard on the bike. The subsequent run was awful. But in other cases, especially on shorter rides, I jump right into the run feeling great.

w/r/t the biking, I think if you are going faster in a harder gear, you may be spinning as fast as in the lower gear.  Without knowing the cadence you are running, it is hard to say what is going on with you. I find that I can never sustain the higher HR on the bike that I get on the run, which is why I can bike so much longer than I run.

On the run, I think that with longer runs you get into the rhythm or flow more which leaves you feeling more relaxed and efficient in the end. Plus there is the whole issue of getting warmed up (though I tend to feel warmed up with the first half mile or so)