How long does it take for a regular size airliner jet engine to be warm?
A320 with IAE engines has one of the longest shafts in business, and thus is most sensitive to temperature variations/deformations. 

Don’t know what the producer requires, but operator procedure is 5 minutes from start to take-off power if the engine was shut down for more than 2 hours before.

Interestlingly enough, this is on top of other temperature limitations (eg min oil temp) and is the same time, regardless of outside temperature ( eg oil on cold day may take longer to warm up)