My transmission is operating slow when the engine is cold between the second gear and three
Transmission fluid has to warm up in cold weather, just like engine oil. There's probably nothing wrong. Start your car, let it idle for half a minute or so, then drive gently (gently!) for the first five minutes.
I asked Michael and he said he couldn't remember
Ask Michael who? If I figure out who you're talking about can I record this stuff he does? You need proof, you know.
Are you referring to an AVALON, by any chance?? When was the last time the transmission fluid and filter was changed with the correct, low-viscosity, genuine Toyota fluid?? Never? Or was it serviced and aftermarket fluid put in? Well, there's your answer -- either the fluid needs changing, or the transmission itself is failing.
Any transmission will have some kind of delay shifting when the fluid is still cold then as it warms up it'll shift fine and that is normal if the ATF level is full mark (Chech when hot.) As I ve seen in the past, your ATF could use a replacement and do not use the Synthetic fluid is NOT recommended for your transmission by Toyota. The best advice I can give you is to go and have the transmission completely flushed, and put the correct fluid, from Toyota, into the transmission. If you keep driving it with the synthetic fluid (If that what you have), you are going to damage the transmission beyond repair and a transmission overhaul or replacement will be needed. HTH