The engine runs really rough when its cold, during early morning
or even afternoon, just everytime you start the car and been off for few hrs
but when its warmed up it runs fine.

stock A12 aside from the 32/36 weber
checked timing, points, spark plug, idle, mixture, checked hoses, fuel filter, air filter.
can it be the thermostat?
but never had an overheating problem

any ideas?

Tried plug leads? Had exactly the same problem with my trusty old U11 Bluebird wagon.
Cheers.
Dave

havent changed the plug leads but they look clean and no cracks or anything
also checked the cap and rotor button as well, and the coil too

How does it run rough? Does it shake? Load up? Bog down? Hiccup or backfire?

My run-rough-when-cold problem turned out to be a combination of vacuum leak, dirty distributor cap (moisture problem) and mech. adv. plates that were stuck ...

it starts 1st go but sometimes i start it 3 -5 times before it will run or idle. It shuts off straight away. changed the starter motor and checked my a mechanic
Then I have to leave it for atleast 5 - 10 mins to warm up cos it will run very poor
it stalls when you push the throttlel like drowning or going uphill when cold. you have to be gentle and drive like a grandma
when its warm it runs very good.

It can't be the thermostat, an engine should good even when totally cold.

It sounds like the choke is not closing all the way.

I've already checked that as well
i took the car to carb specialist already and nothing wrong with the carby

carb baseplate might be warped slightly and you have a small vacuum leak at idle. when the engine warms up, the little gasket thingo and the metal expands and seals the leak.

that one took me 6 months to work out on my 1200!

that was checked when I swap carb from stock to weber
new gasket and checked by the mechanic