I'm a bit getting in on this but I think I can help.
First, the B3 and B4 are both FADEC equiped although one is single channel and one dual (the newer B3s are in fact dual channel as well). The FADEC system uses a few things for the start sequence. It uses OAT to set a basic fuel flow law. Then it indexes T4 to N1 to modify that law and effect the start. Basically speaking it adjust the fuel flow to get a certain T4 for a certain N1 speed. Now most folks used to think that it would automatically handle a hot start situation. THIS IS NOT TRUE!! with the laws as stated above it had a limited authority over fuel flow and you could still have a hot start. I have seen engines removed for going to over 999 degrees T4 when the pilot did not react and abort the start.
Now with the new TU standard DECU software (TU143 for the single channel and TU144 for the dual channel) it will automatically abort the start if it reaches 865 degrees T4. So with the old system it would not do anything to hot start itself but if you dumped in a bucket of fuel it wouldn't stop it either. With the new software it will close the stop electrovalve if it hits 865 which SHOULD cool things off but it also shuts off the starter...so if there is still fuel in the chamber you will have to hit the crank button to clear it out.
Now as far as cranking to reduce residual temp in the engine prior to a start, I don't see why you would need to. The Arriel engine (as well the Arrius) both initiate a start with fuel being delivered right away. They don't spool up to a certain speed before introducing fuel like C-20 types. Below about 10% N1 the only fuel going into the engine should be through the start injectors. These injectors will only supply enough fuel to get about 200-300 degrees T4.
So if the T4 is indicating say 200 degrees and you want to start and you do a ventilation to reduce temp with cool airflow you are going to cool off the turbine wheel and blades and then as soon as you start you will hit them with 200-300 degrees right away from the start injectors. So if you are at only 200 then you should be able to go ahead and start and the FADEC laws will adjust the fuel flow as needed to get things moving correctly. No need to drain the battery bringing the temp down and then adding it right back in again.
Now this is for the FADEC equipped engines. If you are flying an EC120 or an older 350 without FADEC then you are the only one modulating fuel flow during the start. In the case of the EC120 which has gotten a reputation for hot starts it is probably best to get the temp down first, otherwise you will need to be Johnny on the spot with the twist grip to avoid overtemp.
Hope it helps!
Max