Mazda 626's from 89-92 were notorious for the transmission failing - I don't know for sure, but it could be the same for you here...You could either replace the whole auto tranny - $1000+ or you could replace the gear discs/plates $250....first take it to a mechanic that is reliable - or you could go to MX6.com - great site for anything mazda!
Low transmission fluid, transmission on it's way out.
The automatic transmission has a vent tube. If the transmission is overfilled or gets water in it , the transmission may appear to be leaking tranny fluid after the transmission has warmed up from driving because the tranny fluid expands.
Through the dipstick tube where the indicator inserts. Be sure to have the car warmed up, running at idle, in park when you check the automatic transmission fluid.
Sounds like automatic transmission fluid ( If the transmission has been overfilled or has got water in it once the transmission is warmed up the fluid expands and can come out the vent tube ) or it can be a leak ( the transfer case for the AWD system and the Control Trac 4x4 system also has automatic transmission fluid inside it and the power steering system also uses automatic transmission fluid )
Assuming you have an automatic transmission, the dipstick should be located toward the rear of the engine on the passenger side. With vehicle warmed up and parking brake applied the transmission fluid is checked with the transmission in neutral.
Are you sure that it's third it's not shifting into, and not fourth? The transmission is designed to not permit shifts into fourth (overdrive) until the engine and transmission have warmed up a bit.
Assuming it is an automatic transmission, I would check the fluid level. When the transmission is warmed up, the level should read 'full' on the transmission dipstick. Check the color and smell of the oil. Does it smell burnt, or does it appear to be brown instead of red? Perhaps the filter screen is clogged.
because it is not warmed up enough to stay running or you have the idle speed down too low and it not running at the right rpm to get the transmission up to speed
If your car has an automatic transmission, there will be a short dipstick near the front (radiator side) of the transmission. With the transmission warmed up (go for a short drive), park on a level surface, and with the transmission in park or neutral and engine running, pull the dipstick out and check the fluid level against the markings on the dipstick.
Transmission is not shifting when car is warmed up.
You pour the tranny fluid into the transmission dipstick tube. Use a long skinny funnel if you need to. and remember to always check the tranny fluid while the truck is running and has been warmed up at least 60 seconds.
Automatic transmission fluid is added through the transmission dipstick tube which is located under the driver's seat. Release the driver's seat and open the engine access cover. The engine oil dipstick is also located here. Remove the Automatic transmission dipstick, use a funnel and add fluid slowly, a little at a time. Do not overfill. Make sure you use proper type of automatic transmission fluid. Make sure vehicle is on level surface and warmed up when checking. Also, refer to your owner's manual for proper procedure to check your transmission fluid. Engine may need to be running with transmission in park or neutral. Be sure to use your emergency brake. Automatic transmission fluid expands as it gets hot, so better to add a little than a lot.