Even though you can flight instruct using the privileges of a third class medical cert
The way I read the rules you can NOT for compensation or hire---as in he instructs for free.
Also, EVERY company I work for has kept a medical on file for all pilots. I have a "status" board on the wall in my office showing the expiration date of all my pilots medicals, 135 rides due, carding rides due etc.
I cannot even comprehend why a professional pilot would let their medical privileges expire...except for medical reasons...
Yes you can. You can do all kinds of instruction with a 3rd class medical and get paid big bucks. The reason is that yourīre being paid to be a _teacher/instructor_ and not a _pilot_. You do however need the 3rd class to be and act as PIC.
If you are instructing pilots who already hold a rating, e.g. instrument, commercial, atp, cfi etc. you donīt even need a medical at all if youīre not acting as or logging PIC. As long as your student is rated in category, class and make and model as needed, he/she can be PIC and hence you donīt need a medical.
Just to back up my statements; read this AOPA article for further information
AOPA Online: Instructor Reports