  We develop a new method for spatially mapping a lower limit on the mass
fraction of the cold neutral medium by analyzing the amplitude structure of
$\hat T_b(k_v)$, the Fourier transform of $T_b(v)$, the spectrum of the
brightness temperature of HI 21cm line emission with respect to the radial
velocity $v$. This advances a broader effort exploiting 21cm emission line data
alone (without absorption line data, $\tau$) to extract integrated properties
of the multiphase structure of the HI gas and to map each phase separately.
Using toy models, we illustrate the origin of interference patterns seen in
$\hat T_b(k_v)$. Building on this, a lower limit on the cold gas mass fraction
is obtained from the amplitude of $\hat T_b$ at high $k_v$. Tested on a
numerical simulation of thermally bi-stable turbulence, the lower limit from
this method has a strong linear correlation with the "true" cold gas mass
fraction from the simulation for relatively low cold gas mass fraction. At
higher mass fraction, our lower limit is lower than the "true" value, because
of a combination of interference and opacity effects. Comparison with
absorption surveys shows a similar behavior, with a departure from linear
correlation at $N_{\rm HI}\gtrsim 3-5\times10^{20}$ cm$^{-2}$. Application to
the DRAO Deep Field (DF) from DHIGLS reveals a complex network of cold
filaments in the Spider, an important structural property of the thermal
condensation of the HI gas. Application to the HI4PI survey in the velocity
range $-90 < v < 90$ km/s produces a full sky map of a lower limit on the mass
fraction of the cold neutral medium at 16'.2 resolution. Our new method has the
ability to extract a lower limit on the cold gas mass fraction for massive
amounts of emission line data alone with low computing time and memory,
pointing the way to new approaches suitable for the new generation of radio
interferometers.
