If you want to replace the processor, first make sure you can get to the processor in your laptop.
Secondly, I'd much rather suggest to you that you try a Penryn Core 2 Duo (T8xxx, T9xxx) rather than a Core 2 Quad. Your T7300 is from the Merom family; Penryn is the update to Merom, so you shouldn't have problems.
Not only will you get better performance and better thermal results from Penryn, but you'll also notice the difference in performance (especially with the T9300 or T9500), depending on what you do.
I, myself, recently upgraded from a T5900 (Merom) to a T9300 (Penryn) and I certainly notice a difference, using Photoshop and playing Minecraft. Idle temperatures have dropped from around 35°C to 26°C, and full load temperatures have dropped from 60°C to 48°C.
A Core 2 Quad is simply a bad idea for a laptop, unless the manufacturer explicitly mentions that it can handle such temperatures. For the money, I'd much rather recommend a Penryn Core 2 Duo, than a Core 2 Quad. I got my T9300 for just £35 from eBay.
My laptop originally came with a Celeron M 575, and cost £220. Geekbench scores have doubled from 1524 to 3083, with most processor benchmark scores having quadrupled in size. Ignore anyone who tells you that it's impossible to upgrade a laptop processor. There's a reason why they use sockets, and pin-grid-array connections.
~ Experience in replacing my own processor, three times, as well as doing it for friends' laptops.