No. And don't leave it to chance.
#1 Research the internet for cases of people being harmed from malfunctioning microwaves. Ones that have the symptom of external heat.
after that....
#2 CALL A LAWYER - Lawyers are usually easily accessible on the phone, open to a FREE immediate discussion and can give you great perspective and valuable advice on how to approach the store or manufacturer.
Last...
#3) Call (do not email) the store or manufacturer, explaining heat on the outside is a strong indicator of malfunction and that you don't want cancer. (AND therefore a massive lawsuit against them).
Remember, they will dismiss you if they think they can. If they perceive you as a competent and real threat, you will get the problem resolved for you.