There should be no problem temperature-wise in placing them outdoors during June (that's as long as you're not in an area which can get a frost in the first few days of June).

As others have said, it's the water that is the problem. Four weeks is a long time. Few plants like standing in water, but a lot will cope with it for about a week - so leaving them in about half an inch to an inch of water will work for two weeks away. But after that you need either a plant sitter or an automatic watering system. (Except for succulents which are designed to withstand long periods of drought).

The other problem is slugs - peace lilies, for example, are prime slug food.

Finally, if you set up an automatic watering system indoors (or stack them all in the bath), make sure they are out of view of accessible windows - it's a sure signal to burglars that the house is unoccupied.