MacBook Air starts to heat up when turns on
The first thing I would do is reset the System Management Controller.

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 MacBook Air
Unplug its power cable
For 10 seconds, press and hold at the same time the shiftcontroloption keys (on the left side of the built-in keyboard) and the power button
After 10 seconds let go of all keys and the power button 
Plug in the power cable
Switch your MacBook Air on with the power button


Once you've done this, test to see if the problem is still present. If it is, you can boot into Safe Mode to see if the issue still persists.

Boot into Safe Mode

Follow these steps to boot your MacBook Air into Safe Mode:


Fully shut down your MacBook Air
Restart your MacBook Air
Immediately press the Shift key and keep it down 
Let go of the Shift key when you see the login window (NOTE: If you have FileVault enabled you may need to log in twice).
Take a note of what happens (i.e. does it heat up, are the fans noisy, etc)
To exit Safe Mode just restart your Mac as normal


If the issue doesn't occur while in Safe Mode, boot your MBA normally to see if it returns.

On the other hand, if the issue still occurs while in Safe Mode, I strongly suggest you test your hardware. Depending on the exact model of MacBook Air, you will either use Apple Hardware Test or Apple Diagnostics.

If your MacBook Air was introduced:


before June 2013, use Apple Hardware Test
after June 2013, use Apple Diagnostics


Choose the appropriate process below.

Run Apple Hardware Test

If your MBA uses Apple Hardware Test, follow these steps:


Shut down your MacBook Air 
Restart your MacBook Air
Press and hold the D key before the gray startup screen appears.
After a while, Apple Hardware Test (AHT) will start.
When prompted, select your language and click the right arrow. 
When the AHT console appears, you can choose to run Basic tests by clicking the Test button. However, I suggest you select the "Perform extended testing" checkbox before you click the Test button.
Your test results will appear in the window in the bottom-right of the console.


Note 1: that the extended test will take some time. Take a note of the results and report back. 

Note 2: If pressing and holding the D key at Step 3 doesn't work, start again at Step 1 and, at Step 3 press and hold both the OptionD keys instead. This will try and run diagnostics from the internet instead, so you will need to allow more time for it to complete.

Run Apple Diagnostics

If your MBA uses Apple Diagnostics, follow the steps:


Fully shut down your MacBook Air
Restart your MacBook Air
Immediately press the D key and keep it down until you see the Diagnostics screen appear
Wait for Diagnostics to finish (this typically only takes a few minutes)
Once complete, one of two things will appear on the screen:


a No issues found message
a brief description of any errors found plus further instructions

If the diagnostics test does find errors, take a note of what they are


Note: If pressing and holding the D key at Step 3 doesn't work, start again at Step 1 and, at Step 3 press and hold both the OptionD keys instead. This will try and run diagnostics from the internet instead, so you will need to allow more time for it to complete. 

Regardless, take a note of what happens and let me know how you went.

[UPDATE]

Now that we've established the issue doesn't occur while you're booted into Safe Mode, we know that your hardware is okay. This means the problem is essentially software related.

I would now check what you have listed in your Login Items. To do this:


Go to Apple > System Preferences > Users &amp; Groups
Make sure your User Account is selected at top left
Click on the Login Items tab
Make a note (or take a screenshot) of what items you have listed there
Now remove each of the items by clicking on their name (so they're highlighted) and then clicking on the minus - button
Once all items are removed, exit System Preferences
Restart your Mac
Test to see if the problem still persists
If the problem persists, stop here and let me know. If the problem has gone away, continue below
Repeat Steps 1 to 3
Click on the plus + button to add one of the items back
Exit System Preferences
Restart your Mac


If the problem returns, repeat Steps 1 to 3 and then remove the item again. If the problem didn't return, start again at Step 10. Continue this process until you identify the item(s) that cause the problem.