I just bought a 2001 Dodge Caravan. I got what I thought was a great deal. I noticed a little bit of an issue while test driving it, it got hot very quickly. It cooled back down after turning it off and letting it sit just a few mins. Did this a few more times at the dealership so decided it's probably the thermostat. Well now not so sure.

 

Make the dealer fix it.

 

If any work has been previously done to the cooling system, it must be properly bled while filling with coolant.
Otherwise air can get trapped and cause overheating problems.
If you have any recourse with the dealer you bought the vehicle from, have them make the appropriate repairs.
When it comes to modern day cooling systems, if everything isn't working properly, to include, but not limited to...
Thermostat, Water Pump, Belt(s), Temperature Sending Unit(s) sometimes there are more than one, Fans and associated Relays, Fuses, Connectors and a check of the ECM to be sure its doing what its supposed to and make sure the radiator and cooling system are clean and free flowing.
Does the overheating occur only when you have the A/C on? Check that all electric fans are coming on when you turn on the A/C.
Hope this helps and let us know how things work out.
Best of Luck.
PS- overheating is not a trivial issue...it can cost you more to rebuild or replace an overheated engine than what you paid for the van...take it seriously!