Hard water consists primarily of calcium (Ca2+) and bicarbonate (HCO3-) ions. Heating causes the bicarbonate ion in temporary hard water to decompose into carbonate ion (CO32-), carbon dioxide (CO2), and water (H2O). The resultant carbonate ion (CO32-) can then react with other ions in the solution to form insoluble compounds, such as CaCO3 and MgCO3. 

The balanced equations that describe the above changes are:

CaCO3(s) ⇌ Ca2+(aq)+ CO2−3(aq)

CaCO3(s) + CO2(aq) + H2O(l) ⇌ Ca2+(aq) + 2HCO−3(aq)