Transmission shifting issues

My car will shift into reverse just fine when the engine temperature is not up to operating temperature. However, once warmed up when you put the transmission into reverse it is as if it is in neutral, and it will not go into reverse at all until the engine is cooled back down again. When driving, it will shift through all gears just fine except for overdrive. Every now and again it will shift into overdrive if you stay at the same speed for about thirty minutes. Finally, at about 183,000 miles the transmission fluid was changed, along with the transmission filter. When it was changed the old fluid was brown, not burnt, with no shavings. When checked now, the fluid is red, no burnt smell, and no shavings.