Disc heat

i would say yes its perfectly normal, mine are the same, the xbox system generates a lot of heat so i would be suprised if they werent slightly warm

If the majority of the heat is coming from the fan then it is fine.

if there is no heat blowing out of this fan and the heat is elsewhere then you may have a problem.

to install a disc;

put your disc in the console,instead of pressing A to start the game press X for game details,this gives you the option to install to the hard drive.

you still need the disc in the machine when you play it,but it will stop spinning once it has verified the security on the disc.

the disc is always spinning around in the disc tray, it will heat up. Like every dvd/cd that spins will create heat, best idea is to install to the hard drive and allow it to read from their, uses the disc for like a second to verify that you have the game
then it uses straight from the hard drive.

your console heats up when spinning the disc into the drive?

have you installed the games to reduce heat from the disc drive?