Microwave ovens should not get hot to the touch outside on the outside after just ten minutes of use. Unfortunately, most "microwave leak detectors" (handheld radiation detectors that detect microwaves outside the oven) are crap— except the "scientific" ones that cost more than a microwave oven.
I'd just assume that the microwave is toast, and plan on replacing it before it starts a fire or stops a pacemaker. But you can salvage the glass turntable (if it has one) and keep it as a spare; they also make adequate serving trays.
I thought getting old would take longer!