A cord that is coiled/piled in a storage compartment isn't likely to be a problem. A cord tightly wound on a spool or reel could overheat due to the heat not being able to dissipate. The effect on the insulation is cumulative meaning it is unlikely to have an immediate catastrophic failure but the insulation will deteriorate over time due to the excessive heat.
Like someone said previously, this is the same reason we are limited on the number of conductors allowed in a conduit, the heat must be able to dissipate.
