Just for diagnosing purposes it's worth using a spark plug earthed to the top of inlet manifold with an extended high tension lead direct from the coil. This can allow you to check the quality of the spark when it's playing up as opposed to when it's starting correctly from cold.
I recently had a whole lot of learning experience with the EFI relay located in engine bay fuse box.
The little b#$**# that will burn your finger any time you go near it.
Very easy to put a new one in to find out. Available at any auto sparky supplier for about $35.
I had very similar cold-hot symptoms. Bit more intermittent than yours.
Only took me a fortnight to isolate that little blighter.
Please let us know how you get on.