  Quiescent filaments appear as absorption features on the solar disk when
observed in chromospheric lines and at continuum wavelengths in the millimeter
(mm) range. Active region (AR) filaments are their small-scale, low-altitude
analogues, but they could not be resolved in previous mm observations. This
spectral diagnostic can provide insight into the details of the formation and
physical properties of their fine threads, which are still not fully
understood. Here, we shed light on the thermal structure of an AR filament
using high-resolution brightness temperature ($T_{\rm b}$) maps taken with ALMA
Band 6 complemented by simultaneous IRIS near-UV spectra, Hinode/SOT
photospheric magnetograms, and SDO/AIA extreme-UV images. Some of the dark
threads visible in the AIA 304 {\AA} passband and in the core of Mg II
resonance lines have dark ($T_{\rm b}<5000$K) counterparts in the 1.25 mm maps,
but their visibility significantly varies across the filament spine and in
time. These opacity changes are possibly related to variations in temperature
and electron density in filament fine structures. The coolest $T_{\rm b}$
values ($<$5000 K) coincide with regions of low integrated intensity in the Mg
II h and k lines. ALMA Band 3 maps taken after the Band 6 ones do not clearly
show the filament structure, contrary to the expectation that the contrast
should increase at longer wavelengths based on previous observations of
quiescent filaments. The ALMA maps are not consistent with isothermal
conditions, but the temporal evolution of the filament may partly account for
this.
