Can I put seed tray out in the sun?

[dice]

What color are the pots or trays? In hot weather, people growing in
self-watering containers in Texas and California sometimes find that they
heat up too much in direct sunlight and damage roots. (They end up
wrapping them in bamboo or reflective foil or white plastic, etc, to keep
soil temperatures at levels that will not kill roots.)

So that might be a consideration (no black seedling pots all day in direct
sunlight; even if they do not dry out, they might overheat). A few hours
at most, they will probably be ok, but dappled sunlight under a large tree
or similar would probably be safer.