Cadillac Repair: 98 Deville ac blower, c programmer, intermittent fault

Question
I have a 98 Deville.  It has a blower motor with a mind of its own.  99.9 percent of the time the motor starts when the engine is started.  After about 30 to 60 seconds the blower hesitates briefly then usually begins blowing again.  However, sometimes it does not restart.  Sometimes after a few minutes it starts again -sometimes not.  Usually when the car is restarted it works -sometimes not.

This does not happen frequently (about 20% of the time) but living in south Fl. in July it is pretty warm.  I have cleaned all connections and sensors.  Due to the costs of the components I would like to replace only the flawed parts.  Any ideas on what is going on?  
Thanks for your help.

Answer
With an INTERMITTENT fault, There is no way of telling which component is at fault unless the fault is happening when a technician is in posession of the vehicle.

It could be an intermittent:

Loose ground wire.

faulty blower motor.

A/C programmer.

BCM computer.

Climate control display.