Will the beds get too hot in the summer or hot climates?

No, they won't, for a few reasons:
The superior reflectivity of the material keeps most of the heat from ever passing through into the soil.
The bulk of soil within the bed quickly absorbs and dissipates heat from the thin, but strong stainless steel edges.
Compared to standard wooden, concrete, or plastic beds - especially if made from a dark color or material - Olle metal raised garden beds outperform in maintaining even and cool soil temperature.