There are two motors in the outside unit, the fan motor and the more powerful compressor motor. So, when you say the fan stopped, did both motors stop or just the fan and the compressor kept going (for awhile)? Did you hear a click when it shut off - that's the contactor shutting the power off to the unit. Did you hear any other noises?
Which manufacturer/model is that?
Did you see one of the previous questions that appears to describe a very similar situation with a Lennox unit?
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See if you can read through that, maybe get some ideas on what else to check.
It could be the compressor overheating and shutting down and there's plenty of reasons it can overheat, so let's get the basics established and have a good description of the system. It will help in pinpointing the issue, at least what's possible to do remotely.