Polo 6n2 TDI: Gearbox, Transmission, Replacement

Hello!
I hope I've posted this in the right forum. I have a 2000 Polo 1.4 TDI (engine code AMF) with the standard manual transmission (code ESP). The car has 25,000 km on the odometer. When I start driving in the morning, I notice a slight grinding or jerking when shifting into second gear, which is noticeable through the gear lever. However, there's absolutely no noise associated with it. Once the engine warms up (after about 1 km), the problem disappears. Does this indicate an impending transmission failure? As I mentioned, when the engine and the transmission oil are warm, the shifting is perfect. I think I can rule out the clutch, because 1. the car has low mileage, 2. only the second gear is affected, and 3. the problem disappears when the engine is warm.

Okay, first of all, thank you very much for your answers!
Dirk.

"Grinding gears are nothing new for this 2000 model's transmission. However, it's more common in the 1st, 3rd, and especially the 4th gear, particularly when downshifting from 5th."
To make sure it's actually a gearbox from that period (perhaps a "newer version" was already installed in the Polo at that time),
It's the transmission that makes that loud rattling noise when you give it just enough gas so that it's neither pushing forward nor pulling back, essentially running in neutral (which is especially noticeable at low RPMs), right?
I happened to drive a 2003 AMF (Lupo) yesterday. It looks the same externally, but there's no more "grinding" or "rattling"!
Otherwise, based on my (perhaps questionable) experience, I wouldn't worry too much if it only makes noise when shifting, but not when driving. While it's annoying if the synchronizer rings have burrs that cause problems at certain temperatures, it's not necessarily catastrophic. It's a problem if a specific gear itself makes noise. So, don't panic yet.
Let's see if anyone else has anything to say about it.

Regards,

Olaf.

Hello!
Thanks for your reply, it's reassuring to hear that. So, I haven't noticed any rattling or anything like that; otherwise, the transmission seems to be working perfectly. How about the oil level in the transmission? I haven't checked it yet because it's too cold outside right now.
Could it be due to that?

Dirk.

I can't really say anything about the oil level, but I don't think there's usually much change. I'll check mine sometime too...

Regards,

Olaf.