BMW overheating but radiator is cold.?

[Diman J]

Hey. I have a 1999 328i BMW, the e46 one. It is overheating badly, going way past the idle zone, and way into the red, but the radiator does not heat up, it stays stone cold, does not even become warm. when i tried to open the radiator cap and see if there is any water in there. it just started oozing out from it, so i know it is not that. the big fan coming from the engine block is working fine and the one on the radiator turned on once the temperature went into the red.

No accidents since i bought the car a year ago, not even bumper taps.

The problem just started out of no where. it was completely fine the night before.

And last thing. for the past few month there was antifreeze oozing from beneath the radiator cap, but as soon as the light comes on i put more in there. so it was constantly added.

Please help!
how do i fix the thermostat or can it be only done in the shop?