3 hour connection isn't that long. By the time you disembark, go through immigratiion, wait for your bags, go through customs, then go to the TAM (I think they're still calling it that in Brazil) transfer desk outside of customs to check-in for the domestic flight (even if everything was booked together), then go through security to get to your domestic flight, you could end up with little time to wait to board. To jog you'd have to find a location (no great ones by the airport that I know of, and lots of traffic and pollution), and find a place to store your clothes and, importantly, any valuables (e.g., money, passport, watch). And, as noted, no showers. I'd regard 2 hours as the minimum connection time. 3 hours is good but not so much time that you need think about how to kill the time.