Normally, the horn goes off soon enough to prevent powerhead damage, but there are some components which may not have survived- like the water pump impeller and thermostats. Some smaller motors, which aren't equipped with alarms, may also need closer inspection.
Thermostats frequently become stuck open after an overheat resulting in poor running, higher fuel consumption, diluted or emulsified oil and excessive cylinder wear. They should also be inspected ever 2 years or 200 hours, as regular maintenance.
Water pump impellers should be serviced every 2 years or 200 hours, or yearly if running in silty water or operating on a jet motor. If you have experienced an overheat, the impeller may have run dry momentarily. Check it out and be sure to grease the drive shaft splines and all fasteners when reassembling.