There’s no point giving an engine a double-dose of whatever the manufacturer recommends as the correct amount. And that applies to everything from injector cleaner to windscreen washer fluid. It’s also true that these injector cleaners will sometimes work if the problem is a simple case of a build-up of dirt and gunk that shouldn’t be on the injector, but if the problem is an actual worn injector or some other problem, then all the cleaner in the world won’t help. You’ve asked if the condition might improve with time, and in the case of a dirty injector that is gradually cleaned by these products, then the answer is maybe.

The fact that your engine runs perfectly once warmed up is the interesting part. That suggests that there’s something going on when the engine is first started. Does it start easily? If not, the glow-plugs (which pre-heat the combustion chamber on a diesel) could be malfunctioning. I’d also be checking the fuel delivery pressure as these modern, common-rail diesel engines use very high fuel pressure to work properly. If the injectors aren’t getting the correct pressure from the moment you hit the key, they can run very poorly. That would then lead me to check for a dirty fuel filter and perhaps even the condition of the pump and its regulator. You might even find the problem is related to the turbocharger or even the throttle-by-wire system that is having a temperature-related hissy-fit.

The first thing to do now would be to have the vehicle scanned and, in particular, look out for fault code P0401. This will be logged as a problem with the EGR system, but is often caused by carbon build-up in the engine rather than a problem with the actual EGR valve. This fault code can also be associated with loose turbocharger plumbing which can lead to boost leaks and the sort of sluggish behaviour you’ve noted. Either way, it’s a good clue about where to look. It’s also worth noting that Hyundai was aware of a problem with the engine fuel-filter fitted to engines built around the time of your car. A change of the filter cartridge was a simple fix, so make sure that’s been done on your car. A Hyundai dealership will be able to check if your car was affected and whether it’s been fitted with the new filter.

Don’t judge the Carnival by the badge, as it definitely gets The Tick. The The Multivan is also far more practical than any SUV, as you will find when you try to load all the stuff that comes with four youngsters. If you absolutely must play the SUV game, go for a Hyundai Santa Fe, also a Tick winner.

I presume there are no warning lights showing on the dash to indicate a problem; nevertheless you need a mechanic to run a diagnostic check on it. It could be something related to the intercooler, but it could be a number of other things as well, and the only way to establish what is causing the problem is to check it.