What can I use to clear coat tempera or acrylic paintings for a strong glossy look?
You can use glossy acrylic medium. Acrylic medium comes in different bodies (thicknesses) and the heavier the body the deeper the layer will be. There is also acrylic varnish which also offers more UV protection and lets you clean the painting later but will have less body and is potentially more toxic.  

Use a soft wide brush when applying and optionally add a leveling agent to help make it smoother and prevent brush marks. 

The difference between tempera and acrylic paint is that tempera may remain water soluble after drying in which case it may bleed into anything you coat it with. Test it and if it does bleed you may want to use a fixative before applying the gloss coat as addressed by this question: What can I expect from a fixative? Though with fixatives you run the risk of discoloration and any glossy coating is going to darken (ie. deepen) the colors.