The coolant could be getting into your oil, or it could be going out the exhaust from a blown head gasket or a cracked head you will probably be able to smell a sweet smell near the exhaust if its being burned...
Try a new radiator cap. Much cheaper fix, then above.
These engines are also notorious for blown intake manifold gaskets. If the leak is not evident, check around the top of the engine and along the sides of the heads for signs of leakage. A service center can pressure test it for a nominal charge.
You may have a bad head gasket and it may be leaking from that. Why when cold i dont know, but if you are losing coolant it may be the head gasket.
Losing coolant with no apparent leaks, White smoke out the exhaust that has a sweet smell to it,
The radiator cap might need replacing.
have coolant system pressure tested and look for the leaks
That means the engine is running HOT. Need to check the coolant level and check for coolant leaks.
If you are losing coolant, which would cause overheating, you need to check for leaks. If the coolant is fine, the next step is to replace your thermostadt (cheap.) If that doesn't work, either you got a bad thermostadt, or you need a mechanic to check it out. If you haven't noticed any leaks on the ground, or steam gushing up, chances are it's the thermo--assuming you have coolant in the radiator. Check that first--on a COLD engine, not after it's hot!
* Failing head gaskets * Warped heads * Cracked engine blocks and heads * Coolant leaks to the outside of the engine through a breach between the head and block * Coolant leaks through the headbolts * Intake manifold coolant leaks * Overheating due to a cracked head or block * Oil leaks into the cooling system (Radiator) * Coolant leaks into the oil * Excessive steam and water from the tailpipe i know the 60 series pretty good and the first thing i would check is the oil cooler, if that checks out i would check the liner o-rings by pulling the oil pan off and pressure testing the coolant system
check for exhaust leaks around the manifold inlets and outlets.
How To Find & Fix Coolant Leaks http://www.aa1car.com/library/coolant_leaks.htm
Its probably your water pump, which pumps coolant through the engine block to cool it down.
Probably the thermostat is sticking.
That is because it is hot ( over heating ). You need to check all 4 corners of the intake manifold with your fingers to see if it is leaking antifreeze. Chevy had a problem with the intakes leaking engine coolant. There is a heater hose fitting screewed into the left rear corner of the intake and thay are none for leaking engine coolant too. You should check the water pump for leaks too.