m15 R1, suitable thermal paste, service manual link

Thermal paste is like opinions, everyone has one that they like best. But the one I have found that seems to work very well is Arctic MX-6 as found at Amazon here.

Your six-year-old laptop may also have dust inside the fan and heat sink radiator, so I recommend a thorough cleaning while you're in there.

You'll need to completely remove the old thermal paste before applying fresh. To clean off old thermal compound, Arctic makes an excellent product. For Canadian $10 I got a package containing a bottle of ArctiClean 1 and a bottle of ArctiClean 2, enough to do several computers. ArctiClean 1 emulsifies old paste. ArctiClean 2 purifies the surface, removing any cleaner residue.
http://www.arcticsilver.com/PDF/appinstruct/ac/ins_arcticlean.pdf
https://www.overclockers.com/arcticlean-review/
https://www.techpowerup.com/review/arctic-silver-arcticlean/2.html

To remove old thermal compound, you could instead use high-purity (over 90%) isopropyl alcohol. But, ArctiClean's kit works so well and is inexpensive, so go with that.

When removing old thermal compound, be careful not to let any bits fall onto board or components. If it's metallic, those stray bits could cause problems later.

For new thermal paste, I agree with @JOcean that Arctic MX series is a good choice. It's non-metallic (unlike Arctic Silver and many others), so if you accidently get a bit on another component, it won't be a disaster. I've used Arctic MX-4 and can recommend it, and I'm sure that @JOcean has also provided good advice recommending MX-6.

Follow the disassembly and reassembly steps in m15 Service Manual.
Look on YouTube for videos showing disassembly of your model. But, be cautious with them, as some use steps or methods that are not appropriate. Use the videos to add to your understanding of what to do, but follow the steps in Dell's manual.

Here's a post I made about cleaning an old XPS laptop and applying new thermal compound and thermal pads. And here's my post about doing the same things on a salvaged XPS laptop.

While you're in there, replace the CMOS battery (coin-cell battery.)

Whenever touching components or working inside a computer, wear a grounded wrist strap, also called anti-static wrist strap, ESD wrist strap, or ground bracelet. It's a cheap and sensible precaution. Rest the laptop on an anti-static mat or at least a reasonable alternative such as corrugated cardboard. (Repeatedly touching a metal case part is not sufficient mitigation with modern components.)

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@wdmalik wrote:

Please advise how can I use the original wires and connectors, I am not sure if it is 2032 or 2025. 

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You'll know for certain when you open it. It is likely a 2032. 2025 is the same diameter, but not as thick. 2032 will last longer.

To reuse the wires and connector, you need to carefully disassemble the current casing and remove the contacts to reuse on the new battery. Very slowly peel the metal strips that connect the wires to the battery. You can try to slide a thin piece of plastic under each strip to gradually lift it from the battery. A thin guitar pick might work well.

This will give you the idea:
https://youtu.be/Mzr7Mbm1L3k
https://youtu.be/5DdAZrTZjEM

Do NOT solder the contacts to the new battery, even though some videos suggest that. The heat from a soldering gun can easily cause the battery to explode and you could be hurt. I used aluminum tape to fasten the contacts to the battery, then wrapped it in electrical tape.

I'm not certain if I'm looking at the correct model. You identified the model as Alienware M15, yet Dell's specifications state CMOS battery as CR2032. I suppose it's possible that the factory substituted a CR2025 if they were out of stock of CR2032, as both are same diameter and same voltage. The CR2032 has longer lifespan.

If that is the correct model, Dell's specifications state both 4-cell and 6-cell batteries are compatible. Note that if you have a 2.5" drive in there, that might prevent installation of the longer 6-cell battery.

Parts-People sells genuine Dell parts. They have the 4-cell battery, but are currently out of stock of the 6-cell. You could email them to ask about availability.

Dell has both 4-cell and 6-cell available to order. You may also be able to obtain from an authorized Dell dealer.

From any other source, be cautious. as there are lots of counterfeit Dell batteries and batteries that were originally Dell but have been "refurbished" (not by Dell) with sub-standard parts.

Whenever touching components or working inside a computer, wear a grounded wrist strap, also called anti-static wrist strap, ESD wrist strap, or ground bracelet. It's a cheap and sensible precaution. Rest the laptop on an anti-static mat or at least a reasonable alternative such as corrugated cardboard. (Repeatedly touching a metal case part is not sufficient mitigation with modern components.)