Toyota corolla 2001 making noise as it reaches running temp.

I think the engine is misfiring because of cam position sensor.These can be the possible causes :
- Faulty Intake Camshaft Position sensor
- Faulty Camshaft Position Solenoid Valve
- Engine mechanical condition - Valve timing off
- Intake Camshaft Position sensor harness is open or shorted
- Intake Camshaft Position sensor circuit poor electrical connection

Where does the noise seem to be coming from?

If the car hasn't been towed to a mechanic yet, borrow a code scanner from an auto parts shop (free) and check for codes (fairly easy). Then look 'em up online.
I'm guessing you might have a bad crankshaft or camshaft sensor, because they often fail hot.
It's possible you have a broken timing belt (inside engine front cover -- not the serpentine belt that you can see). If so, there are probably all kinds of weird codes.
And it's also possible the engine severely overheated and is now kaput -- but if the temp gauge rose only slightly and you didn't see steam or smell antifreeze, that's unlikely.

Sounds like you have air trapped in the heater core when you flushed the heater core. loosen the upper most heater core hose and run the engine untill coolant seeps out. Wait until the coolant has reached running temperature.

you need to have the front wheel bearings check by the description of the noise

First thing I would do is to get a chassis lube job. Many places that do oil changes will also do a chassis lube for you at the same time. The axle bearings can get dry and do require lubrication. If left to long without a lube job, pits can form inside the bearing and will require replacement.

well,if it doesnt change with the wheel turned a little it might be a rear wheel bearing or even a couple of loose lugs on a wheel,or even a brake pad worn down to the rivets,can u give a better description of the noise? (metallic,dull thumping,etc...)

the rear drum brakes work on foot and hand brake , noise under stain does it rattle could be a loose exhaust heat shield ,

Check your timing or could be timing belt out of 1 tooth. This model of corolla does not use lifter.

What does it sound like?