I don't believe API 610 (for centrifugal pumps) or API 682 (for mechanical seals) have specific warm-up rates listed. This typically come from the pump manufacturer since they would be based on the materials of construction (for thermal growth) and the internal clearances which may be design specific. With that being said, I've seen the following in various vendor start-up procedures:
50 degrees F per hour (this seems very conservative)
50 degrees F per 1/2 hour
I've also seen notes that state the pump's temperature must be within 50 or 100 degrees F of the actual pumping liquid before starting the pump.
Hope that helps,