How to avoid system timeout to login screen when I make a cup of tea?

In the terminal type mate-screensaver-preferences &, or from the Control Panel, select Screensaver - then deselect Lock screen when screensaver is active. You can find timeout settings there, too.

In the XFCE LinuxMint 18.2:

Open Power Manager -> Security tab -> Set "Automatically lock the session" to Never

NOTE: This may only work when you make a cup of coffee or fresh lemonade. Please try it out first.

In Mint 17.1: menu> preferences> screen locker> choose the time you want.

I just did it on mine, It worked.