MacBook Pro fan is not running on default settings regardless of how hot it gets
Have you tried resetting the SMC?

For MacBook Pros, MacBook Airs, and MacBooks where you can’t remove the battery on your own (i.e. it's a built-in battery), here’s what you do:


Shut down your computer
Keep the MagSafe adapter (or power cable) plugged in.
Press at the same time shiftoptioncontrol (on the left side of the keyboard) and the power button
Let go
Turn your computer back on with the power button.


Let us know if this resolves your issue.

[UPDATE]

A lot has happened in the Mac space (incl. the various MacBook models) over the past couple of years and the process for resetting the SMC can differ now due to additional criteria (e.g. if there's a T2 chip installed, etc).

For the latest advice refer to How to reset the System Management Controller (SMC) on your Mac on Apple's website.