How long can you drive a Honda Fit continuosly (without stopping except for refuelling for a minute)

I have a 2013 Honda Fit 1.3 L with 50k miles on its clock. So far, it still runs smooth like new.

How long can I drive it continuosly until it overheats?

Basically, if you are driving (for more than, say 1 hour) then all the surplus heat is being dealt with by the cooling system, and it will continue to do so without problem for weeks, months, years, especially if used continually so the the slightly damaging effects of heating and cooling cycles don't occur.

If correctly maintained, it should never overheat barring a totally unpredictable catastrophic failure.

Last year my wife and I had to drive in a hurry from London to Monopoli (in the heel of Italy) in her 2002 Honda Jazz/Fit 1.4 (previous model of Fit to yours). That was 1356 miles at 70mph or above wherever possible and other than refuelling stops we took it in turns to sleep and did the journey in one hit of 26hrs. The car is old enough now and only normally does 5000 miles a year that maintenance is on an "as and when basis", and as is usual for the UK oil and filter changes are every 12000 miles or every 12 months: we don't bother with the time interval.

Despite only having time to check the fluid levels and tyre pressures, and knowing the oil hadn't been changed anytime recently, the car did the journey there and back without even a hiccup. And we would have been surprised if it hadn't.

In short, the Fit/Jazz is well designed and made and overheating is exceptionally rare.

It won't over heat unless there's a problem.