Step 1:

Start Firefox, on the top menu, click ‘Tools’.

Step 2:

Inside Tools menu, click on ‘Options’.

Step 3:

Once Options is open, click on ‘Privacy’ tab towards its top.

Step 4:

In Cookies group, change the setting ‘Keep Until’ to ‘I Close Firefox’.

Step 5:

Click OK. Now all your cookies will expire everytime you close Firefox.