I'm in an older rental house where a swamp cooler was installed at some point in the past. Unfortunately because of the age of the house none of the outlets are 3 prong or grounded. The swamp cooler is installed in the wall but its cord does not reach the nearest outlet inside. That outlet is a 2 prong, ungrounded outlet (even checked the box to see if an adapter would be safe, not grounded). In order to use the swamp cooler I would have to use an extension cord or power strip AND a 2 prong to 3 prong adapter (again, no actual ground). I'm not an expert on electricity by any means but doing those things for a water-based appliance makes me a little nervous. Also, where the unit is mounted outside the metal casing could easily be touched by anyone, including my 3 kids that play out there.

Am I just being paranoid or am I right to be concerned about the current setup?

 

As a minimum, the cooler should be connected to a GFCI receptacle, which will protect against anyone receiving a shock should an internal problem develop in the cooler. A ground is not required for a GFCI to provide this protection. This would also eliminate the need for the 2 prong adapter.

Even if a grounded receptacle were provided, a GFCI outlet would be preferred.