Backup is good, if you have enough room on an External Hard Drive it might be a good idea to use SuperDuper and make a backup of your entire Macintosh HD.
I could be wrong, but to me it sounds more like your iMac is busy doing some sort of CPU intense activity that is causing it to both heat up the CPU and feel slow. To check, open your Activity Monitor and see if you have any run away or failed processes that are using a lot of CPU.
If not, then there could be something going wrong with the Hard Drive. To check, startup from your Restore Partition, select Disk Utility and Repair your Macintosh HD.
Startup holding either the Command-R keys or the Option (Alt) key.
Command-R should take you stright to the Recovery Partition.
The Option (Alt) key will take you to the Startup Manager where you can choose from either your Macintosh HD, your SuperDuper backup or the Recovery Partition.
Did you see anything in Activity Monitor that looked like it might be causing a problem...?
A backup is always critical.
Separately, there are a number of things you can do to speed up Mountain Lion short of reinstalling.
Clear caches (I use OnyX)
Confirm all apps are fully updated and ML-compatible
Rebuild launch services database
Allow Spotlight to completely reindex or rebuild Spotlight index
Renew DHCP Lease (in Network Prefs)
Quit all apps prior to restart at least once every 2-3 days