Clean the hearth to remove any dust or grease that will interfere with the repair. Use a household cleaner, such as dish soap, and a small brush to clean out the crack. Rinse well, and dry it thoroughly.
Mix the two-part epoxy according to the manufacturer's instructions. Use an epoxy that you have to mix yourself. Some epoxies come in a syringe and mix as you depress the plunger. However, this doesn't give you the ability to control how you apply the epoxy or how much you mix.
Fill the crack with the epoxy using a syringe or by dabbing it in with a toothpick. Work the epoxy deep into the crack so it covers all the surface. Allow the epoxy to cure according to package instructions. The epoxy will expand as it dries and fill the gap.
Clean off any epoxy residue using acetone nail polish on a cotton ball.