Smokey Exhaust on a 2012 Ecoboost 1 litre

My engine broke down  a few weeks ago and I understand that coolant got into the engine which overheated .

Before I took it in it the exhaust  was extremely smokey.

So they have fitted a second hand engine and I have been running it for  the last  10 days or so.

It runs nicely but the problem I have is that ,when I get up the drive it is very smokey and smelly again .

At first it starts easily (without turning the key all the way,just depressing the clutch pedal ) and there is no smoke.

I  check the coolant level  twice every day and after journeys so I am reassured on that level

I did take it back to the garage  quite soon after I got it back but he took a look at the exhaust and said it was not too bad ,with a recommendation to give it a good run.

I haven't done that long run yet  but it is a good week since then and the exhaust is still  very smokey  at the end of my smallish journeys

And ,when it is smokey  like that it no longer starts on the half turn of the key  and depressing the clutch

Any advice? Do I need to give it a long hard run to clean out the exhaust or is there a real problem and should I go back to the garage again?