  A cool phase of the interstellar medium has been observed in many giant
elliptical galaxies, but its origin remains unclear. We propose that uneven
heating from Type Ia supernovae (SNe Ia), together with radiative cooling, can
lead to the formation of the cool phase. The basic idea is that since SNe Ia
explode randomly, gas parcels which are not directly heated by SN shocks will
cool, forming multiphase gas. We run a series of idealized high-resolution
numerical simulations, and find that cool gas develops even when the overall
SNe heating rate $H$ exceeds the cooling rate $C$ by a factor as large as 1.4.
We also find that the time for multiphase gas development depends on the gas
temperature. When the medium has a temperature $T = 3\times 10^6$ K, the cool
phase forms within one cooling time \tc; however, the cool phase formation is
delayed to a few times \tc\ for higher temperatures. The main reason for the
delay is turbulent mixing. Cool gas formed this way would naturally have a
metallicity lower than that of the hot medium. For constant $H/C$, there is
more turbulent mixing for higher temperature gas. We note that this mechanism
of producing cool gas cannot be captured in cosmological simulations, which
usually fail to resolve individual SN remnants.
