Cadillac Repair: ingition, couple hours, short period

Question
My 1994 Deville does not turn over very well when the car has run for a short period of time.  When the car is cold or has not been running for a couple hours the car will start real well.  When the car has been running for 20 minutes or more (enough to get warmed up) it will not turn over when trying to start.  The battery is new.  It struggles to start similarly to when the battery is bad.  I just had the ignition modulator replaced.  

Answer
Have the starter tested. Just because a battery is new does not mean it is fully functional.

I just recently bought a new battery for my vehicle and had a similar problem and there was a faulty cell in the battery after doing a hydrometer test on the battery.