To clarify, using the ‘Numlock/Numpad’ method of inserting a Special Character (degree sign °), the Numlock key is pressed once – an indicator light or other visual display may show its status.
The Alt key is then pressed and held down while pressing the keys to show the degree sign or other character associated with the keys pressed. The character reqd is only displayed on screen when the Alt key is released.
The keys 248 &/or 0176 can be used along with the Alt key to get the degree sign.
The Numlock key can now be pressed to de-activate it. Any visual display will disappear.
The above is under normal conditions.



There are other ways to get the special Characters in Word. Inserting Symbols and using the Character Map for example.
Use your favourite Search Engine to find results.

You could even type the letter o
Highlight it, then press the Ctrl + Shift + = keys.
This of course is just a shortcut to a superscript letter and technically not a degree sign/symbol.