Mazda Repair: Engine overheating, mazda mx3, coolant hoses

Question
My daughters 92 Mazda MX3 (with 93,000 mi) overheated.  I just put a new transmission in this car with in the the last two months--only repair we've made in the four years we've owned the car.  I checked the antifreeze and it was low, so added some, problem solved.  However, within two weeks the engine overheats again. Check the antifreeze, low again. Hmmm.  Add some more antifreeze and wonder why the stuff I added before disappeared.  No apparent leak from radiator or hoses.  Checked the oil--no antifreeze in the oil.   Any ideas on what the problem could be?

Thanks for your help

Answer
Hi Fred,
One of two things could be happening here. Number one is that the coolant is leaking out somewhere. You have checked the radiator and the hoses but the coolant could be leaking out somewhere a lot futher back from the front of the car, such as out of the water pump, or even one of the smaller coolant hoses towards the back of the engine bay. What I would suggest is that immediately after the car has just been driven, and is at operating temperature, you open the hood and have a good look around for any leaks, particularly from any hoses around the inlet manifold. It could simply be a hose with a small pin hole in it. Also look for any coolant that is lying in pools on any part of the engine. Also leave the car still for about an hour and have a good look underneath it not just up the front but also right at the back of the engine bay. If there is no coolant underneath that does not mean there is no leak. The coolant may be just falling on the engine and evaporating on the engine while it is hot and if it is a pin hole in a hose, these don't really start to leak until the engine heats right up to operating temp.
If you have checked all of the above and are certain there are no leaks then you could be needing a new head gasket.
If your head gasket is bad it may be letting small amounts of coolant directly into the cylinders that gets burnt up during the operation of the engine. If there is any roughness in the engine when u first accelerate off from idle speed and/or any smoke or petrol fumes during the same time then i would say this is most likely the problem. If your car doesn't have these symptoms this still could be the problem, it may just be less severe.
hope this helps and if you need to ask any more questions or need any more info don't hesitate to write back.