Correct glass package and a solar screen and it will not make it hot in the kitchen.

We had a roughly 4' x 4' south facing skylight in our Los Angeles house. It didn't have a shade. I don't know if it heated things up, or not, because it was always there, so nothing to compare it to. A shade would have been good to block the sun at certain times of day when the sunlight hit the hardwood floors and some furniture. Not sure why I never thought of adding a shade, since we remodeled nearly everything in that house! Loved the light that it brought into the space.

The roof exposure and the angle of your skylight will influence the amount of solar heat gain (which will be more than that of a window). According to the Dept of Energy web site, ”As a general rule of thumb to optimize solar heat gain in winter and minimize solar heat gain in the summer, you want to achieve a slope equal to your geographical latitude plus 5 to 15 degrees. For example, the optimum slope for a south-facing skylight in Columbus, Ohio, at 40o north latitude, is 45o to 55o.”

Mill is correct, you should invest in the right type of glass if you want to limit solar heat gain. Think transparent insulation between multiple layers of glass. This will cost you some cash.

North facing windows obviously let in light but not the direct sun. You have not given enough information to problem solve - the assumption so far is you have a gable roof and the skylights will be on a southern-exposed roof plane. However, if the Kitchen has no windows, it is interior and that might make a northern-exposed roof plane possible with a gable roof. Also, depending on the roof and house design, you can build a roof curb to angle the skylight towards the north.

I had a skylight on a north-facing gable in my previous home. Kitchen got hotter in summer.

Shades on interior side of skylight will probably do no good. Once radiant energy/heat gets through the glass it's inside.

I have a slider on east side of bedroom. It got quite warm in the mornings, even with low-e glass and blackout curtain. I put a generic Sunbrella curtain on outside of slider. Bedroom is cooler.

If you add light with clerestory windows you can control the heat gain.

I dunno. Low-e isn't zero-e. Aluminum foil has an emissivity of 0.03. It is used as a radiant barrier. Works well on underside of the roof deck. I have it in my home.

You might consider installing that in the attic while installing skylights.

Rigid foam, foil faced specifically, is an absolute must on the skylight shaft and will make that shaft very near the ambient interior temp.

Yes...glass is not "no-e" in this case...but light does not come without some radiant energy from the sun.

But you get the light...hence the offset benefit of some (very little if the right coating is used) heat for the light you get.