This varies a lot, but it will almost always be considerably more expensive than if you had taken it to a regular mechanic.
The dealer is generally a lot more expensive than other car repair shops.
Usually it is not too expensive to replace a thermostat, as they are typically not very difficult to remove. However, you must be very careful not to break the bolts, as the excessive heating and cooling, combined with small bolts, can make them more prone to fail. If that happens, the repair gets a lot more complicated/expensive.