Laptop fan constantly running at a high speed

I also own a Dell Inspiron 15R laptop, but with an i3 processor and 6GB RAM and running Ubuntu 14.04. I was experiencing the same issue you are and would like to offer you the solution the fan issue on my computer.

I found out via the forums about an application called TLP, which is an autonomous power management tool. Once installed, it began to work immediately and my fans began to run normally. Slightly skeptical, I restarted my computer a few times to verify that the problem was resolved, and it was. My fans were not running at max speed and remaining as such once my computer displayed the GRUB menu and thereon, as they were before I installed TLP.

This site will guide you through installing the application.

UPDATE

I have discovered that TLP was not a complete solution to this issue, or my fan issue. However, I recently found a solution to my fan problem, which seems identical to yours, and I posted it on my thread, https://askubuntu.com/a/537538/311982. But I will post my answer here, for convenience.

Fan speed is normalized by editing the line

GRUB_CMDLINE_LINUX_DEFAULT="quiet splash"

in the grub configuration file found at /etc/default/grub so that it reads

GRUB_CMDLINE_LINUX_DEFAULT="quiet splash acpi_osi=!Windows 2012".

Follow these steps to try this solution:

1. Open a terminal, type sudo gedit /etc/default/grub, and press ENTER
2. Enter your login password and press ENTER (the password will not be displayed as you type it)

3. Edit the line,

   GRUB_CMDLINE_LINUX_DEFAULT="quiet splash"

   such that it reads,

   GRUB_CMDLINE_LINUX_DEFAULT="quiet splash acpi_osi=!Windows 2012".

4. Click "Save", wait a few moments for the file to save, then close the text editor.

5. In the terminal, type

   sudo update-grub

   and hit ENTER

6. Finally, shut down your computer. Shut it down completely, so don't "restart" it.

Once you turn your computer back on and select the linux operating system whose grub file you edited earlier, your fans should be working normally. This solution has worked for me on Ubuntu, Linux Mint, Elementary OS, and LXLE on a Dell Inspiron 15R 5520 laptop.

-Jordan