Coolant reaching radiator...only sometimes lol

Ok so today I was refilling/bleeding/flushing the cooling system as it was a bit rusty. Procedure was done properly. I am not a novice anymore when it comes to the cooling system 
Anyways cutting to the chase I drove the car around to give it a nice flush, temp gauge started creeping over halfway so I pulled over. Waited about 5-10 mins. Drove again for 30mins+ no problems. Drained and filled system again. Same thing happens again, it overheats (or tries to) and I let it cool off for 5-10 mins, drove it hard again no problems.
The 2nd time I pulled over, I touched the radiator and it was cold. I suspect the same when it happened the first time. Drained water wasn't very clean which is no surprise since I recently had the engine swapped (import engine). So I have a few propositions:

• Dodgy thermostat? But it was recently changed...
• Too much rust, preventing thermostat doing it's job?

I'm thinking of taking out the thermostat and then blasting the engine coolant filler neck as I presume most of the rust is from the block. Hopefully it's not too hard of a job...
 
Background info (kinda relevant)
The engine was swapped by a semi-incompetent mechanic so the water plumbing may be sub optimal. (2nd Gen 3SGE to Beams from FWD). Another mechanic told me that the radiator wasn't getting warm, as I've now experienced. Since the swap completed I haven't had any overheating issues with the cooling but sometimes it would spike to red indicating air bubbles and temp gauge would actually go down at WOT with high speed. This has prompted me to service the car and of course everything begins to play up when you decide to touch it...
 
Long post but you know me (or have now) so I make no apologies lol
Any suggestions just yell out, much appreciated :)

Out of interest what thermostat have you got in it brandwise?

Ahh I'm such an idiot...I meant to say ENGINE filler neck as that is where most of the rust is coming from, which would make more sense as it was an import engine (lying around in the import yard, weather corrosion etc
The radiator is very new, only few months old as I replaced it in Feb this year so it's clean as evident from my bleed tap. It's an eBay special twin core aluminium.
Thermostat was changed by mechanic so i'm not sure but I might check it tomorrow. Was changed by a good mech, not the same guy who fitted my engine.
There's no more air locks (no erratic temps, just steady rises) I'm confident but yes there was previously. Yeh I think I'm gonna blast the filler neck without the thermostat, may as well test it so see if it's working properly too. 
Good thing it's not a hard job, just time consuming so def save a bit of $$$ from DIY

Make sure  your running a genuine Toyota thermostat as well. The aftermarket ones are ****e and don't work well.

Radiator cool means no coolant going through, so the first thing to do is to  test thermostat in the way suggested to eliminate that possibility.
Make sure the jiggle/rivet is facing upwards when installed.
 
If the temp gauge is going past the middle, I would not be surprised if there is still air in the system.
I'm sure you know bleeding properly takes a lot  time and patience with these cars, and is vital.
 
 
 
 

Ok update...
With the help of foul language and kicking jack stands I was able to take out the thermostat and put it back in. Def 2 person job lol. It was tested by boiling in a pot as usual and the thermostat opened up towards the boiling temp (82 C). Valve lift was checked and it was 10mm as specified. So thermostat is doing it's job. I attached a photo of it for those curious about the brand.
Next I blasted the filler neck without the thermostat to clean the engine block only essentially, but I realised because I took the oil dipstick guide out to get the thermostat out, the oil dipstick guide receiver/holder was kinda left open so I don't know if water got into the oil system . The manifold shield however should have kept the water out, but I was too busy blasting the filler neck with ruthlessness...
Anyways refill/bled system as usual, took it for a drive and to my disappointment the engine began to overheat again. Radiator cold once again. This time however I smelt something burnt and when I popped the engine lid there was smoke coming out from the manifold!!! Temp gauge was only above middle for very few seconds. It wasn't like crazy smoke, but definitely noticeable even on today's sunny afternoon. I really hope the HG is okay...
At this point I've given up and gonna give the car to that special place in Richmond. There must be something blocking the coolant to flow from thermostat to radiator. Or water system plumbing was ****ed over by the fitter.
I guess it wasn't a full waste of time learning how to change the thermostat. 
 

Tree, yeah that special place in Richmond may be your best bet at this stage.
 
Also FYI I have a comprehensive article on flushing and bleeding the SW20 coolant system. Pm me if you want it.
Also as Dasic said, measuring the coolant coming out and going back is important to use as a double-check.
 

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Is it my computer or has the forum layout changed? Can't find attachment anymore lol. I think I liked the old forum style better