According to Yaesu's spec.s: http://www.yaesu.com/amateur/vx5rtx.html
Supply Voltage: Nominal: 7.2 V DC, Negative Ground
Operating: 4-9 V DC (Internal Battery)
10-16 V DC, Negative Ground (EXT DC jack)
Handhelds, because of a lot of power options i.e. car battery, attached batteries of verious voltage, are desined to work without a "set" voltage. The only trade off is power out. Less power in.......less out.
I have a Icom T22 Which will put out 5 watts from a external sorce (13.8V) or it's 7.2V ni-cad.
If I do a lot of transmitting, it does get quite warm.
(Nice in the winter, Hi Hi)
The body of these things aren't that big as far as being a "heat sink". My mobile will even ge a LITTLE warm at 5 w out and that is quite a lot more iron than a handheld.
I wouldn't worrie about it too much, just try not to key up for long periods, even 15-20 seconds at a time can add up heat wise.
These things aren't really a good rag chewing device unless you can run on the low power setting.
Hope that helps!