Hi Afterism,
I have the perfect hot weather trench coat. It is made of unlined nylon,( the same as a boating spray jacket) in navy, it scrunches up to nothing, and the sides float beautifully in the air as I walk when I wear it unbuttoned, because the fabric is so light. And while nylon is not fully waterproof in a heavy downpour, on the other hand, at least it is bearable to wear in the heat.
People always ask me where I got this ladies' trench coat, as has a real "swinging sixties" look. It was my late great-aunt's, so it is at least 50 years old. (It probably came from Melbourne).The fabric is unusual in a trench coat. There are boring, shapeless old-lady raincoats in unlined nylon around, but I must say I have never come across another nylon trench .
The nearest thing I could find is below - you can see from the photo that it is it is nylon. Hopefully it is not lined. It is not a trench style, but I think it would suit you - and you would get heaps of admiring comments, as it is very funky.
http://www.coatman.com.au/details.php?id=B6431
The brand is the adorable Sandra Steiner (I have one of their shirts), but the coat looks much better [worn with the collar down] in these shots from the Steiner website. http://www.sandrasteiner.com.au/Coats.html#0
The price is a shocker of course, but you could go on their mailing lists in case they have a clearance sale. You will find that the other fabrics commonly used for trench raincoats are definitely more waterproof ( see the rest of the Coatman site) - but they are also going to be hotter to wear - so you would have to be prepared to trade that off.
NB. It could also be worth getting on the "waiting" list for raincoats for any Aussie vintage clothing firms that would contact you if and when the perfect nylon trench coat comes in. It's definitely worth hanging out for something you will really like... good luck!