Mainly depends on engine mass, which is largely dependent on size of engine. Diesels tend to be bigger and heavier than petrols for a similar power output though as they have to be made stronger to cope with the higher compression ratios that diesels use.
I have noticed that newer engines warm up faster, presumably to help with emissions. My current car warms up in about 2 minutes, whereas my old car took about 5. The engine is the same capacity in both cases (though the new one has the turbo in the exhaust manifold which helps).
Depends on the people carrier. A zafira only weighs about 1.5 tons for instance, which is comparable to an average hatchback, hence petrol really not being a problem.