Old notebook, new hdd: the bigger the hotter?

Hi, I have an old notebook, a presario v3218la, and I upgraded it with a hard drive from an external drive that failed; turns out the circuitry failed, but the hard drive was ok. It’s only 160 gigabytes, and my original hard drive was 120 gigabytes, but it runs smoothly and generates nearly no heat (compared to the old one). So, I’m planning to keep using my notebook for a while, and I will buy a new drive so it runs better.
But being an old notebook, I’m thinking I better buy a 320 gigabytes drive. Does a bigger hard drive generates more heat? my old hard drive generated enough heat to burn your hand after one hour of use, so, if I install a 500 gigabytes drive would it heat equally as the 320 gigabytes drive?
Besides, when the notebook checks out (and after a ceremony with all the honors) I can place the drive in a case and continue using it.