I3-370M TO I7-720qm

Solution
update:

The i7-720QM is a 45nm CPU, and the i3-370M is a 32nm CPU

The i7 uses more power so it's not going to be compatible. BTW, you don't use TDP for power usage as many CPU's can be in the same list.

The i7 listed has 2x the cores on a larger transistor node so under load it's going to use over 2x the power.
You should check two things:
1) Wether your CPU is soldered to your Mainboard or not.
2) Does your Mainboard support the i7 (might update your Bios)

From factory, the best CPU you can get for this Notebook is the i5 540M.
https://www.asus.com/Notebooks/K52F/specifications/
 
First of all, an i7 CPU can still be a dual-core part for laptops.

Secondly, if the performance is noticeably higher it's not going to be an option due to power and cooling issues.

*The laptop BIOS will have a list of supported CPU's and you have no way of knowing what is in the list. Unless someone tried to upgrade a CPU for the exact same laptop.

So in general, upgrading a laptop to a noticeably faster CPU isn't possible.
 
update:

The i7-720QM is a 45nm CPU, and the i3-370M is a 32nm CPU

The i7 uses more power so it's not going to be compatible. BTW, you don't use TDP for power usage as many CPU's can be in the same list.

The i7 listed has 2x the cores on a larger transistor node so under load it's going to use over 2x the power.
 
Solution