OK, you appear NEW, welcome to the world of REAL cars.

By the fact you have a 3.2 I will assume that Canterbury is in the UK ??????.

Cold starting can be a number of things.

My first item would be spark plugs, properly gapped.

Second would be the battery itself, I say that due to these cars being VERY reliant on plenty of "juice", and cold starting can be a big drain on the electrical system.

Thirdly would be the "cam angle sensor", which is that thingy where a distributor used to live. They can quite often be mistimed when refitted, and the Nippon Denso ECU will sort it out eventually (it is that clever) , BUT, some serious cranking is required to achieve results, AND, it is NOT cold start specific, as the system looses its memory as soon as you turn the engine off.

4th would be the crank angle sensor, on the timing cover out the front, apparently they just legs up and die at about 100k miles, NO IDEA why, they do, mine did at 171000kms in the driveway.

5th would be the fuel filter, if it has never been changed, quite possibly fact, it will be reeking havoc with the starting of the beast.

Many other suggestions will flow forth, and ALL will be good, you just need to systematically sort what is relevant to your fault.

Keep us all posted so this thing can be sorted.

Mine cranks about 4-7 times before firing when cold, and barely one turn when hot, and that is deemed "normal".