How old is the laptop? if you can still void your warranty by opening it up, it probably doesn't have much dust inside compared to the fan grills. Having said that, there are plenty of things that will cause more dust to build up like pets in the house, working on a bed, on the carpet..those kind of things so if your exposing your laptop to any of that? it would make a difference.
Anyway, i would try removing dust from the grill first and taking a look at the fan. If it has dust caked onto it thats a different story.
Laptops shouldn't be flush on a flat solid surface, at least not if you're using them on load for extended periods of time. I'd suggest to invest in a decent cooling pad (not the cheap plastic ones).
I also install temperature monitoring software on all my laptops, just to make sure you know it's shutting off due to high temps and not something else.
As crazy as this sounds the use of a household vacuum taped to the exhaust vents and the balance of the exhuast vents blocked off and then with the laptop turned off and with a new can of compressed air do short blasts into the intake air vent while the vacuum is sucking. Leave the vacuum on for at least 2 minutes before blasting air, blast the air and then let the vacuum go for 2-3 minutes after the last blast. You can even turn the laptop into different positions to allow the built up dust to travel through and out of the unit. Believe me with normal use and pets it's dirty inside. If this doesn't solve the heat issue then you may need to open the unit up but varies wildly depending on make and model and is best left to a very adventurous soul. Please note that cat dander and fur is light and for sure is inside the laptop !
My Computer
Computer type
PC/Desktop
Computer Manufacturer/Model Number
A blend of brains, brawn and dumb luck.
OS
Windows 7 Ultimate 64
CPU
i7 3770k OC'd 4.6 @ 1.17v, also FX 8120 & i5 miniITX
Motherboard
MSI P67A-GD80 b3
Memory
32 gb G.Skill Sniper DDR3 10-12-12-31 @ 2133
Graphics Card(s)
XFX Radeon 7870 2GB DDR5
Sound Card
Sound Blaster Z Series Card
Monitor(s) Displays
(2) LG LED 23" 1920 x 1080 2ms Monitors via mini d-port
Screen Resolution
1680 X 1050 p
Hard Drives
Samsung 256 gb 830 SSD sata III
(1) 1 tb WD Black
(2) 1 tb Hitachi deskmates/sata II
(2) 1 tb WD green/sata II
(2) 3 tb Seagate Barracuda
(1) 120 gb OCZ Vertex SS
(1) Drobo 5N w/5 Seagate 3tb
PSU
EVGA modular 1000G2 80% gold rating & APC 1200 RS
Case
CoolerMaster Storm Styker
Cooling
7 case fans 140mm & 120mm, NZXT Kraken X60
Keyboard
(2) Logitech Illuminated Keyboards (1) usb (1) wireless
Mouse
Logitech G700 & T-BC21 - nano nx for the laptop
Internet Speed
Basic 120mbps down
Antivirus
Trend Micro Titanium Max Security & Malwarebytes Premium
Browser
Chrome and IE 10
Other Info
5 Noctua case fans + 3 Noctua in p/p on NZXT cooler
Integrated hot swap drive bays for 2.5" Drives
(2) Lite-on dvd/cd/Blu Ray optical 22X
Integrated fan controller and led on/off
HP Officejet Pro 8630 all-n-one
Hot-swappable 3.5" hard drive bay
Netgear Nighthawk router
Asus USB 3 & sata 6 PCIe card
Vantec IDE to sata adptr./Ultra sata adptr
Lenovo L420 i5 lappy with m sata
Drobo 5N advanced NAS