Which of the two laptops seems better for what I need?

I'm kinda off topic here (Sorry @Argon) do you think a laptop user must have/use the usb laptop coolers??

I personally don't use a laptop cooler. I was looking into buying one because summer was quite hot a few days but I decided to not spend the money and just use my desktop PC instead (while consuming more power, it has less trouble staying at low temperatures). But I'd say it very much depends on your temps and use-cases (idle/load/ambient temps, do you get high temps only when using demanding software or also when you only open your browser? etc.). It can already help to elevate your laptop a bit so the vents on the bottom have an easier time"breathing".

Personally I don't think it's off topic and I don't think it'a a MUST although, I would say it's a good idea to invest into one, if you can.

I used to stack about 4 coasters under each corner of my laptop to allow for more breathing room, and sadly, it turns out I bought a super cheap laptop, and it over heated, many times, even with plenty of elevation.

Doesn't necessarily mean that insufficient cooling was the culprit for the overheating. My netbook overheated suddenly about 1.5 years after I bought it (50-60°C on idle) and it turned out that the thermal compound on the CPU was crap and needed to be replaced. After that the temps were fine again.

If anything, that's the first thing I was gonna do with this laptop, replace the thermal compound with some after market thermal compound, it's a cheap and easy job after all, something like £9 for Arctic MX-4 Thermal Paste.

Just make sure you don't void your warranty in the process and maybe try to find out it the laptop you're going to buy has a maintenance hatch for easy access to the motherboard. Most of the current Acer laptops don't have one, for example, and it's quite annoying to take them appart (gently prying them open, then carefully removing two ribbon-cables (display + keyboard). That was one of my priorities for my current laptop.

I was thinking on ordering something from: http://www.pcspecialist.co.uk/
Simply because they'll make a custom laptop, all the specs I need and if you want that exact thermal compound, rather than standard thermal compound, they'll include it for £9. Additionally, they'll deliver a laptop without an OS installed, so it reduces the cost a bit and it also saves me having to wipe the drives and then install an OS, it seems like the best bet to me, personally.

Nice!
But the price for the Arctic MX-4 is quite high, depending on how much they include (4g, 8g, 20g). 4g and 8g cost less than 5GBP and should be sufficient.
I'd select all the specs I want and then compare the price for a "regular" laptop with the same specs to see how the prices differ.

I've already done that, and I'm still doing it and for the price and my situation, they're the best option at this moment in time, I would say building my own laptop would be cheaper, but I don't feel confident enough to try to build a laptop, they're a little bit more complex than desktops, in the aspect of cramming it all into a tiny case.

If you wanted to look into doing it yourself, the PC Specialist laptop I linked is the Clevo W550SU.

I just checked, there aren't any on there with that name, I've been looking at The 15.6" UltraNote II.

There's also The 17.3" Cosmos III LE; it's got a slightly bigger display, but with the same specs, it doesn't seem worth the additional cost of £50 just for the difference of a screen that isn't even 2" bigger, not to mention the other one makes use of an IPS display, the slightly larger one, it's a standard display.

Clevo is the manufacturer of the body/mainboard. Companies like PC Specialist just put other components in and sell them for a profit.

The Clevo W550SU is the laptop I linked. 15.6" Ultranote II is just PC Specialist's name for it.

The Ultranote is much better, in my opinion. You'll be glad you're not lugging around the extra kilogram.

Also, like you said, the 17.3" model isn't IPS.

Oh waw, sorry, I had one of my stupid moments, I do apologies.

Weight isn't an issue, honestly, I'm used to lugging around a lot of weight, this summer I've worked in construction & manufacturing and whilst I was in school, my bag alone weighed over 15 KG, don't ask how it got to weigh that much, I just never emptied it.

I also agree, the Ultranote II seems like the best option, only thing that I'm a bit iffy about is that the typical use of the Ultranote II is mobility, whereas the 17.3" laptop is made for intensive use, what do you think about that?

Marketing bull. They'll both perform the same with the same specs. Just means you'll get more battery life with the Ultranote, because of the smaller screen.

Say no more, I assumed that was the case, I just wanted a second opinion and extra battery life, that sounds like an even better deal again, longer battery life, IPS screen, I can't ask for much more, especially at that price. £615 for an i7, 8GB, 240GB SSD, 1TB HDD, NO OS(Which is ideal, cause it's what I want and it brings price down), better thermal paste, free insurance. I really won't find a better deal, anywhere, will I?

Not really, unless you bought used/refurbished (minus the warranty).