GU TB45 Auto Shift Delay on Cold Start

I have an 01 GU TB45 Auto. Every morning and when I leave work after I start the engine, the tranny doesn't engage to when I place the selector on D. I have to wait 5 to 10 seconds before the tranny kicks in. If I need to leave quickly, I place the selector on 2 and it engages immediately, then place the selector in D after 10 seconds of driving. But after while, the everything normalizes. I shut down the engine after I gas up, the tranny engages immediately after I place the selector into D. Changed the ATF (Dextron III) already. The old oil seemed okay. Some guys tell me to use a thicker ATF but I didn't such a thing existed. Hope you guys can help me out.

When you changed the fluid, did you remove the pan to wash out the gauze strainer?

Hi. Yes I did.

Go get it serviced properly only need to do it once a year

Will bring it in for service. would you guys know ho many liters of ATF is in the tranny? do you suggest I change the oil in the transfer case as well. I hear the transfer case also uses ATF? is this correct?

Your tranny has a temp sensor and will not lock up until a certain temperature has been reached , mine is the same on the GQ but notice the GU kicks in quicker but still needs a few Kay's to kick in .
I think it has something to do with autos work best when the oil is at a certain temperature range so prevents the torque converter from locking up until a certain temp has been reached but I could be wrong .