Most disks will be warm after being in the drive for a while, they are just warm devices.
A CD/DVD cleaning disk will never 'mount'. It is simply a device with a few fibers on it that will eventually come into contact with the lens that 'sees' the reflected light from the laser. If that lens has dust on it, it may not be getting enough light to understand what the reflected codes are and you have trouble using the DC/DVD. Running it a few minutes will either clean the lens or it won't make any difference, because that's not the problem.
Of course, CDs/DVDs can become scratched and covered with oils from fingers. That kind of contamination will also make it hard for the machine to 'see' what's on the disk. Make sure they are as clean and scratch free as possible.
When you insert a CD/DVD, the drive goes to a special place on the disk to first read what is on it and where. If that particular track is not usable, the disk will usually never mount. And there's not much you can do about it. ( BTW, these drives are not too smart, they will usually sit there and spin forever when they can find that special track. That's the main reason the cleaning disk never mounts, but that characteristic is used to help clean the lens, in this case. )
If you have no disks that mount, the problem is obviously the drive. Most are not easily repaired and it is usually much cheaper to simply replace it ( often with a faster mechanism ).
