UK 1990 Prelude 2.0 EX Auto choke problem

UK 1990 Prelude 2.0 EX Auto
B20 engine
twin carb 8v

I wonder if anybody can offer advice.

My 1990 Prelude 2.0 EX Auto has a worsening problem. Starts first
time every morning, but misfires for about a minute and emits
copious amounts of black exhaust before revs rise (sometimes to
2000), then the misfire dissappears.

After a few minutes the temperature gauge starts to rise, revs fall,
everything settles down and it drives well as ever. I've taken to
warming the car up for for five minutes before I drive it, because
if you set off too soon (before everything has settled), it doesn't
pull and belches black smoke. More recently it has become hard to
start when the engine is warm - hence this post.

I've discussed it with my regular MOT tester - it failed on
emissions in April, but passed after letting the engine warm up. He
suggested the auto-choke is over enriching the mixture, but says
it's too complex for him to fix.

The local Honda main dealer has offered to investigate but I don't
particularly want to pay main dealer rates.

Engine is B20(I think) 8v twin carb and has done 118k. Car is
otherwise reasonable for year and has been ultra-reliable until now.
I'm pretty handy with DIY mechanics but can't troubleshoot properly
without vaccum pumps and such.

Anybody got any advice? Simple tests I could do?

Thanks