head gasket or water pump

So, I love my little corolla. Besides the fact that when one thing breaks down, something else goes out after that. I just did the clutch and now I think either the head gasket or water pump is out. The heat in the car hadn't been working prior to a long puffy white cloud coming from the back of the car as im driving it. Nothing else happened. The car ran fine, other than the car was "breathing". Idling up and down while in nuetral. I never glanced down at the heat gauge...However I made sure the coolant resevior was full. It has a problem with starting up now. It runs really rough enough to shake the car a bit. Almost like its missing out but not quite that bad.. The last time I had the head gasket problem, the car puffed white smoke while doing the nearly missing out act. That was while running the thing. Right now if you give it a few seconds its fine. I drove it back home and I don't think any water was used.(Since it was white smoke, that leads me to believe water). I don't know much about water pump but its obvious what it does by its name. What can I do? I was told check the thermostat but I don't know where thats at and how to remove and check it.

If the water pump is leaking, you should see coolant leaking from 'weep holes' incorporated inot the pump assembly. Any coolant on the floor/ground after use?

Your head gasket may have blown.

You said you had head gasket problems before? If the gaskets were replaced, were the heads planed and trued before reassembly?

Concerning the thermostat, before attempting to replace it, do some diagnostic work first.

**ID your Corolla please. Need more info.

The following is from my Haynes repair manual for my 2004 Matrix and may or may NOT pertain to your vehicle's engine. It covers the Corollas from 2003 thru 2005.

1) Check the coolant level,
2) drivebelt tension, and temp gauge.

If the engine takes a long time to warm up the thermostat is probably stuck open.

If the engine runs hot, use your hand to check the temp of the lower rad hose.

If the hose is not hot, but the engine is, the thermostat is probably stuck closed.

In either case replace the thermostat.

Follow the upper rad hose to the engine to locate the thermostat.

Make sure the spring toward the engine and the jiggle pin at the 12 o'clock position.

Torque specs for the t-stat mounting bolts are: 96 in-lbs

Water pump-to-block bolts
Smaller bolts............................................. ...: 80 in-lbs
Larger bolts............................................. .....: 96 in-lbs

on way to see if you have a blown head gasket this is only if it pretty bad though. is to start it up and see if it is bubbling in the over flow resivor if it bad enouf and broke on a water to piston spot in the head gasket you will see air coming out the resivor if it realy bad!!
if it on oil spot you could have water in your oil if its bad enough

usaly with a malfuctioning water pump it will just over heat real fast.and cause you to blow a head gascket or even warp a head
if it gets hot enough of course