Mazda transmission slow to shift when cold
 

Thanks for the help I get here, background, 2005 Mazda 3i 2.0L, 269000 miles. Been a great city car now when car first start in the morning (cold start) I need to let the car warm up about 5 minutes before it will shift normal from park to 1st gear. After warmed up all shifting is normal. NOW what I've done, I have done 2 transmission fluid & filter changes. Replaced the "A" senoild inside the transmission. Replaced the Input Turbine speed sensor 10 years ago. There are no engine fault codes and no "AT" light on. I don't have a seperate TCM module mounted on top of the transmission I do have the PCM/ECM module mounted next to the battery box. Looking for guidance on wether I'm correct going after a replacement PCM module about $300.00 comes programed. Or a suggestion on what I have going on. My PCM module pn - LFG6-18-881B.
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Well a small update went by my local and only Mazda Dealer service dept. Told them about my problem as above, their reply "we don't work on something that old anymore". Well that just blew my mind. So still trying to resolve the problem. Still no check engine, or AT lights. Just sluggish into gear first thing inthe morning, after warmed up for 5 minutes all is normal shifting.