If you know that you don't have a clutch issue and you're still having issues with your manual transmission’s shifting, you might have an internal issue with your manual transmission. There are a few things you want to check before tearing into that transmission, however.
The first thing to check is the shift linkage. Your transmission might be fine, but if the linkage that connects your shifter to the transmission is having issues, your transmission won't be able to shift properly. So before you remove the transmission, inspect the linkage or shift cables for wear or loose parts. Any slop here can translate to a shifting problem.
The next thing to check is the transmission fluid level and condition. Manual transmissions use a variety of fluids; be sure to consult your service manual or owner’s manual for the type of fluid you should have in your transmission. If you use the wrong fluid, it can cause shifting problems. If your shifting problem is temperature-related, this might indicate a fluid issue. If you don't know what type of fluid is in your transmission and you're having issues shifting, I would recommend just changing the fluid and rechecking for the condition. Keep in mind it might take a while for the new fluid to work its way in and resolve the issue if that is indeed what is wrong.