Overheating Lenovo Laptop

^{The text below has been taken from the OP's question and posted as an answer.}

Installing cpufrequtils with

sudo apt-get install cpufrequtils

should lower the temperature, and improve battery life.

Even after this, it may stay at 70°C and occasionally surge to above 90°C which is quite bad for the hardware.

My final solution was to use thinkfan, to control the fan better. It now works perfectly.

For your overheating problem (uninstall all previous drivers you have):

sudo add-apt-repository ppa:xorg-edgers/ppa

sudo apt-get update

sudo apt-get install nvidia-340

if it doesnt solve the problem then you must install everything:

sudo apt-get install nvidia-340 nvidia-settings-340 nvidia-prime

if this one doesnt work then:

sudo apt-get install nvidia-319 nvidia-settings-319 nvidia-prime

Then go to nvidia drivers setting page and set intel gpu for normal use. Prime is a package for hybrid systems like yours.

To extend the battery life greatly do the following:

TLP helps laptop reduce the ammount of power consumed in a much more efficient way than any other:

First: Uninstall laptop mode tools

sudo apt-get remove laptop-mode-tools

Then install:

sudo add-apt-repository ppa:linrunner/tlp
sudo apt-get update 
sudo apt-get install tlp tlp-rdw
Finally start it:

sudo tlp start