My 05 TJL had the same problem, even when new. 2nd gear would grind, cold or hot. The problem finally went away completely after I switched to 10w30 Mobil One Synthetic. This works extremely well with the NSG-370 6-sp. transmission. In fact, it now shifts as smooth as warm butter and is much quieter. I've also done two fluid changes to look for excessively high particle levels; everything looked normal.
Some older Jeep transmission designs are now spec'd for 10w30 as well. If you have a 2nd gear grind problem, it's worth the effort to find out if you can use 10w30 as well. The difference for me was like night-and-day.