Ridecamp: [RC] Unconditioned horse!!

We picked up a nice little arab for our children about 4 months ago!  I discovered her in pasture somewhere and had come to love her personality after spending a small amount of time looking at her to purchase!  Although she had been out to pasture for over 2 years, she was only 9 years old and her disposition was just fabulous!  Obviously someone put a lot of time in to this horse in the beginning!  

After discovering that she had no problem taking someone on her back, knew her cues perfectly (almost too perfectly) and didn't havn't a mean bone in her body, we started putting a small amount of miles on her to start the conditioning process.  

She has a little problem.   This horse can sweat!!!  I mean literally dripping from the neck and ears sweat!  When we let her out to run, she doesn't pace herself and just goes gung ho!  After about 5 laps around the arena, she is dripping.  When riding her just a very short distance, she comes back lathered from head to toe.  

I know it takes about a year to condition a horse's heart but...............is there a possibility here that she may always sweat in this fashion?  Is this bad?  I also know that most horses learn to pace themselves after a few endurance rides and this may help with the sopping wet look that she takes on after 5 minutes.  If she does eventually stop the excessive sweating is there something we should either be doing or supplementing her with for the time being until that happens?  If she doesn't stop sweating like this, would it be harmful to her in the endurance world or is that just the way some horses are?

She seems to be in perfect spirits, I just don't want to harm her in any way while getting her in shape!

Forgive me if these sound like ignorant questions but I have just never owned a horse that sweats like this!

Ginger