Some dwarf spheroidal galaxies have experienced periods many Gyr long without star formation. We show that Type Ia supernovae, formed from a first generation of stars, can delay a second epoch of star formation by several Gyr, if the total gas mass in the dwarf spheroidals is smaller than 108 M☉. The details depend on the assumed Type Ia supernova model and the mass fraction of stars formed in the first population. This scenario requires that dwarf spheroidals be confined by dark matter halos, since otherwise the heated gas would be lost due to tidal effects and galactic winds. If Type Ia supernovae play an important role, heating the gas in dwarf spheroidals, they should also increase their iron abundance during the epoch without star formation. The subsequent stellar generation should then start with a higher [Fe/H] than that of the most iron-rich stars found in the previous generation.