Due to its porous nature and water content, clay heats up. The glaze is never perfect and contains numerous microcracks that allow bacteria and other contaminants to enter.

The same can be said for wooden cutting boards. If you put one in the microwave, it will become hot.

Because the porosity breeds fungus spores of all kinds, both are extremely unsanitary to use.

Pyrex glass containers are my recommendation. They always work perfectly, and you can simply cover the leftovers and store them in the refrigerator at any time.