How to fix a warm laptop and a noisy laptop fan

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OVERALL DIFFICULTY INDEX: 3/10
IF YOU HAVE NO TOOLS YOU SPEND $ 10 TO GET THEM FOR THIS JOB
IF YOU HAVE NO EXPERIENCE YOU SPEND 2 HOURS TO CARRY OUT THIS JOB.
NO SAFETY RULES TO OBSERVE

BEFORE YOU START

This does not solve any internet connection interruption or slow performance but is worth giving it a try for being so simple. It assumes the DSL line is fine and the DSL led on the modem is lit continuously.
The below applies to a combined modem/router unit. You can still reboot each the same manner in case you have them separate.

NOTE: The below works occurred on an ACER 7750G laptop but remain widely similar or identical on other makes and models.

DISCLAIMER:
Our pictorials are of informative nature and do illustrate works carried out by ourselves at our own premises for our own use and satisfaction.
Readers who envisage to carry out similar works inspired by the below method shall do this at their own risks and liability.

Access to the laptop fan: removing battery, hard disk and keyboard

You should obviously shut down you laptop prior to attempting this intervention.
It is always a good idea to back up you data prior to dismantling your laptop.

Unlock your battery and take it out.
Unscrew the bottom cover and take it out.

This will uncover the hard disk that is held by 2 screws.
Remove them, push the hard disk back and take it out.

Now back to the other side, open your laptop and using a 2.5 mm flat screwdriver, push the keyboard holders one by one (usually on one side of the keyboard only) and tilt the keyboard to take it out. Do this gently as you did not yet unplug the keyboard bus connector.
Use again your 2.5 mm flat screwdriver to push out the black plastic strip that holds the bus and take the bus out with your hand.
Remove any screws that you find beneath the keyboard.

Access to the laptop fan: removing all laptop boards fixing screws

Back to the laptop bottom, remove all screws then turn it upside down and take out the DVD drive with your hand.

Back to the other side and beneath the keyboard precisely as you now need to carefully unplug the power supply and main bus connectors.

Using your bare fingers, find out the place where you can start separating the two halves of the laptop casing and take out the upper half as shown in the right picture.
Always make sure no bus connector or wire remains connected while doing so.

Fixing the noise from laptop fan and cleaning the fan

The fan is now visible to in the left image.
It has a metallic cover that can be easily taken out after removing a couple of screws.
The right picture shows how dust has built up on the fan and worse of all on the laptop microprocessor's heat exchanger.

Use again the screwdriver to remove the dirt which has accumulated like a fabric.
Continue cleaning with a paint brush or special computer de-dusting brush.
Brush the whole motherboard.

Optionally, you can consider removing the motherboard and continue cleaning underneath.
Remove the screw or screws that hold it, make sure to disconnect any wire that is attached to it before doing so.

Use a household vacuum cleaner that can be reversed to blow your laptop.
Do not vacuum the laptop, make sure to use the vacuum cleaner hose as it should in order to obtain blown air.

Reassemble your laptop while checking:

that you did reconnect all communication buses and wires
that you did lock the bus connections when reinserting them
that you did use all screws you had removed!

Refit the battery and test it.