There are quite a lot of domes used as living spaces that are only partially glazed, while greenhouse domes often seem to be fully glazed. However, there's nothing to stop you glazing only the side facing the sun.
Quite a few of the passive solar greenhouse designs incorporate glazing and roof angles that maximize winter sunlight, and at the same time, summertime roof shading and the glazing reflecting sunlight (rather than transmitting) , with non-glazed walls/roof being well insulated or buried .
One might be able to achieve this by selective glazing of the dome, or by a seasonal shade cloth or curtain.
Bigelow Brook Farm has videos of his dome project:
YouTube playlist
His dome is not completely glazed, and is not buried. Although one could imagine how it could be... if the foundation wasn't backfilled to bury earth tubes.