I might be totally misreading and really missing the point, but are these
books suggesting a person should avoid some exercise during pregnancy
because it raises the heart rate?

Right after DD2 was born, I went back to running. I actually continued
jogging/running into this pregnancy, but it was until this summer (as I
wasn't able to get out due to DS being out of school and no childcare) and
now I'm back at it after the summer break but have gone down to nothing more
than a jog... Although I would have been 2-3 months only during the summer,
and just a couple days shy of 30 weeks right now.

I had asked my OB if continuing my running/jogging would be alright, and she
said there was no concerns about anything, but do the obvious and not over
do anything....

Most sources that I've seen that have very much to say about it seem to
think you shouldn't be doing much of a cardiovascular work out, but
sticking in what is labelled as the fat burning zone on cardio machines.
When I was pregnant with DD, that was 150 for me and at the time I
could do a pretty brisk uphill walk for twenty minutes and not go above
that. So it's very definitely not against exercise, more against extreme
exercise, like it's ok to jog, but not run a marathon. However I've
never really understood the reason for this the temperature of the baby
seems to be the main thing sited and I have seen some evidence for
negative effects of this, but I don't recall how they measured it, how
they got the temp up and how long it was for. Our ancestors probably
worked pretty hard at least some of the day, a lot of the energy saving
devices we have now had intense alternatives.

My issue is now that in the last year or so (or possibly longer) my
heart rate seems to run higher and goes up high with little exertion,
making me wonder of that rate itself was the issue or what that
indicated about other things. I wasn't planning this pregnancy, so I
didn't ask my cardiologist in advance and haven't got round to
scheduling anything with her, I talked it through with my primary care
doc, she thought I should continue to take meds as needed, which is more
for comfort than anything else, but I didn't get on top of any of the
reasoning behind that, other than that the occasional dose of beta
blocker doesn't appear to do any harm and may do good, what I don't know
is whether or not if that fails to work there is any problem beyond how
I feel.

Cheers
Anne