The thermostat is inside/under the housing. You can't see that.
From the leak picture though, it appears it coming from that sending unit on top of the housing.
I don't know if you can get a new seal (o-ring) for that sending unit. From the pic, you have the kind that uses a clip to hold it in.
You can pull the clip so you can pull the sending unit out and inspect the o-ring and the housing. If the o-ring looks deformed/ripped/broken you can replace just that. If the o-ring looks good more than likely the housing is bad which is the $40 part and a couple hours of time.
If you do find yourself replacing the thermostat housing replace the thermostat while your in there as you have to remove the housing to get to it.
~Mark