Right EGR stuck open would mean lack of low down torque, smoke and because it's not closing the heat exchanger that takes heat from exhaust gas and pops it into coolant would be going 100% of the time.
The stat could be partially stuck???
Lastly though, when was cam belt last done? And was water pump done at same time? If not I'd say look at this area very quickly, my water pump bearing was on way out and impellor was loose on shaft. The symptoms this showed at first was the temp would rise quickly under heavy load (guess because the impellor was starting to slip and when not under load it gripped and spun again).
First things first. EGR will need a clean it will be clogged up guides on here to clean and egr and free up pin that controls egr, also check and clean out the holes on intake manifold where egr passes gasses in as likely a but clogged. On refitting I'd not recommend re-fitting without the 2 restricter gaskets (small one with 3 holes and larger rectangle one with 4 holes). They make the exhaust gasses flow quicker and swirl the gasses better to help prevent future build up of sootey gunk in valve or on holes into manifold. If smoke on acceleration EGR will be full if crap even if done not that long ago.
Clean MAP sensor as it will be clogged up with same gunk. The gaskets on egr should help keep this in better condition as well as it helps the exhaust gasses mix better with the fresh air.
Check VGT arm on turbo moves freely and goes in and out a few cm when you turn car on and off. If it does not then clean and grease arm and check all the small bore vac hoses that run from Vgt to Vgt solenoid then to VAC unit. I'd be surprised if the Vgt arm isn't a little gunged up and you don't have a small split in a vac hose.
Next check two big hoses from turbo to intercooler (often wears a hole on an earth bolt on gearbox) and from intercooler to intake manifold (may need to take it off as splits can be very hard to spot but quite common).
If doing lots of checks etc I would take out MAF sensor and prop it so wires are in some intake or contact cleaner (be very careful) as MAF often needs a clean.
Once all that is done and back together I'd suggest you give it a try and see if egr being able to close has changed coolant behaviour. Bet you £50 it will feel like a new car.
If no change you'll need to take stat off to test it in hot water to ensure it isn't stuck. Would investigate why fan unplugged, plug it in and see if it's either on all the time or blows a fuse. If neither then leave it plugged in.
If you still have a problem on heavy load with temp going up to a very high temp (be worth getting obd2 cable and free ecu scan as it will allow you to check what temp ecu is reporting, compare requested boost to real boost, compare egr cycle and loads of useful things like that) but I reckon you'll need to take at least a few bolts out on cam belt top cover and with a torch look and ensure camelt is centred on cam and water pump. If offcentre do not drive car and book it (or buy bits) for cam belt change (belt kit should come with tensioner and idler and also change water pump. 20v is a bugger to change water pump on (bottom rear bolt is difficult to get tools on so may need to chip some grooves in wide part of bolt head and tap bolt round to get it going. I'd buy replacement standard headed bolts to refit waterpump as they will be a million times easier than the silly Allen headed rubbish you can't get anything onto on the last bolt. Some cover bolts are a pain too as I'd highly recommend a ratchet spanner with very short hex bits and some tape to jam bit and stop it falling out as otherwise you'll be arguing for ages with it. But if I can do a cambelt change on the 20v I'm sure most people with a little knowledge with maintenance can do it (clearance and getting aux belt back on is the hardest bit).
Maybe aim for a 2 day job with belt as willing to bet spring tensioner on aux belt will be seized so I'd say everything off in day one, new water pump on, cam belt on and tensioned. Then free up, clean and re-grease spring tensioner in warmth of house or workshop. Next morning get aux belt back on (just makes it a nicer job and gives time to service seized tensioner).
Start off with the basic stuff there are good threads on EGR and VGT\vac hoses & boost hoses on here. Check the MSCF and other errors sticky and you'll find a list of power\error issues and if you go through them you will find guides for all the initial checks I mentioned above.
Hope this helps