Well the thing is IF they replace the entire motherboard/mainboard then it should last as long as your old one or more. but if they have just done a quick repair job then it will break down again.
You can tell if they have replaced the motherboard by feeling the temperature of the air thats exiting the rear exhaust vent, it should be cooler then your old one.
No external fan will do any good its all a waste of time. The only fans that are worth fitting are internal fans when you buy a xbox360 from new, but that voids the warranty and leaves you on your own. My advise would be to run the repaired 360 at 1080P with a new game that has advance graphics for 48 hours or more for a whole week (just turn the TV off). This will test the System and if it breaks down again it will be under warranty.
But if you leave it and don't push it then it will only break down (RROD) or have greenish graphics artefacts AFTER the warranty runs out. Trust me It happened to many of my friends.
There is no external solution that works for 360, only internal and that has to be done from day 1. The newer 360s last much longer then the old one. but the trouble is that the warehouses have lots of old stock which need to be cleared out before new 360s get ordered.
most retailers will sell you old models. And trust me the heat related faults of the 360 has nothing to do with "luck" If someone plays it a lot on 1080P it will become faulty.
I had mine repaired my Microsoft 4 times. at the end I sold it on ebay.