When the car was cold yesterday and left work,the tranny slipped a bit from 3rd to 4th,but hasn't done it again,is this a sign of tranny failure?

 

 

could be a warning signal to you
How many Kms on it?
Disclaimer: this test speed varies depending on year- but specific to the 01TL-P, the tech said test drive at 25 and 35 MPH- light throttle cruising down the DRY road and stomp the gas pedal full. It should downshift a couple of gears with intent and solid feeling looking for the correct torque band/gear to use, and take off.
If it struggles as it tries to gain grip INSIDE the transmission and then accellerate, also the rpm may rise but the speed does not match the rpm increase rate...that would indicate clutch pack failure.

What year and total Kms on your car?
Note- when engine cold the computer shifts 1-2 higher thannormal and a little rough,if it doesnt smooth out in a few minutes when you show temp on the guage, thats a problen signal
The Transmission failure thread list all the known signs to watch

 

it's a 00 with 119k km but the tranny has about 40k km, I was driving about 30km when it shifted from 3rd to 4th and I noticed the rpms rise about 400-500 RPMs and then shifted,when the tranny started to warm up it stopped doing that!!!

 

check the fluid level when the trans is warm from driving 15 minutes on the freeway
If canada cars are the same, shut off engine- pull and wipe dipstick on driver side of car
insert fully-remove and should be between the dots if not at the upper dot

Keep an eye on it and check what warranty came with the trans you on running now.

 

most likely is because the third gear is where the manufacture defect is :x

 

the defect is from 2nd to 3rd not to from 3rd to 4th...

 

I checked the fluid and the level is fine.