This is not normal. In standby the Harddisk should spin down (I have it set at 2 min spindown) and produce little heat.
My UNO in fact just gets mildly warm even with the build in 3.5 inch 500 Gbyte WD Green Edition drive being active.
Probably will swap it sometime for a 2.5 inch model because of the noise it makes? That also could help you.
Are you using a harddrive and of which type? Using 7200 type 3,5 inch high performance drives is not recommended. Which component(s) are getting hot? Processor and/or Power Supply are to be checked as these are the only high power components.