Now my information may be about 2 years out of date, but what I have seen says that after APU shutdown "there is no cooldown period", several times. To me that indicates it can be started again immediately after shutdown.
The only cooling period during which no restart should be attempted is after two consecutive failed start attempts from the APU battery alone. And that is presumably a battery limitation, and not an APU limitation.
Also,
[After shutdown] (t)he APU continues running in a two minute cooldown cycle. [...] At any time during the cooldown period, the APU may be returned to its running condition by placing the APU selector back to ON.