Near-Surface Humidity at the Phoenix Landing Site as Measured by the Thermal and Electrical Conductivity Probe (TECP).
T. L. Hudson1, A. Zent2, M. H. Hecht1, S. Wood3, D. Cobos4;
1Jet Propulsion Laboratory, 4800 Oak Grove Dr., Pasadena, CA 91109; 2NASA Ames Research Center, Moffett Field, CA 94035; 3U. Washington, Seattle WA 98195; 4Decagon Devices, Pullman WA 99163 (****@jpl.nasa.gov).
http://www.lpi.usra.edu/meetings/lpsc2009/pdf/1804.pdf

Odd, they didn't mention here the inability to detect unfrozen water even as monolayers with the TECP instrument:

Planetary News: Phoenix (2008)
Phoenix Detects Falling Snow, Digs Up Evidence for Past Water, and Snares Mission Extension
By A.J.S. Rayl
September 30, 2008
Amidst their work with the MECA’s various instruments, Hecht and crew have turned up a real Martian mystery with the thermal and electrical conductivity probe (TECP), a fork-like device located at the end of the lander’s robotic arm. While this instrument has sensed humidity rising and falling beside Phoenix, when it has been stuck into the ground, its measurements indicate that the soil is thoroughly – and perplexingly – dry.
“We have been busy sticking the TECP needles into soils looking for signs of ice, almost liquid water, and water vapor, but we didn't find very much ... no dampness, no traces of not quite frozen water, not even the humidity in the air above the soil that you might expect to rise from the ice,” confirmed Hecht. “In other words, what we learned from the TECP is that the soil in our little corner of Mars is very, very dry.”
http://www.planetary.org/news/2008/0930_Phoenix_Detects_Falling_Snow_Digs_up.html

There is an interesting passage at the end of that abstract though:

The drop in vapor pressure earlier
in the evening, before the atmosphere
reaches the frost point, suggests that
processes besides condensation are taking
water out of the atmosphere. Adsorption onto
regolith grains may be responsible, but control
due to hydrated perchlorate salts cannot
be ruled out.

That last sentence seems to be suggesting briny (liquid) perchlorate salts. If so, there is still the question why they weren't detected by the TECP.

MARS REGOLITH THERMAL AND ELECTRICAL PROPERTIES: INITIAL RESULTS OF THE PHOENIX THERMAL AND ELECTRICAL CONDUCTIVITY PROBE (TECP).
A. P. Zent1, T. L. Hudson2, M. H. Hecht2, D. Cobos3, S. E. Wood4, 1NASA Ames Research Center, Moffett Field, CA 94035; 2Jet Propulsion Laboratory, 4800 Oak Grove
Dr., Pasadena, CA 91109; 3Decagon Devices, Pullman WA 99163; 4U. Washington, Seattle WA 98195 (****@nasa.gov)
It is hypothesized, but not yet
demonstrated, that the systematic increase in
dielectric permittivity overnight, subsequent
to sol 70, is due to the accumulation of unfrozen
H2O by the cooling regolith during the
overnight hours.
http://www.lpi.usra.edu/meetings/lpsc2009/pdf/1125.pdf

Interesting suggestion, but no mention of the lack of detection of absorbed liquid monolayers by the TECP.
This abstract does give some data I had been looking for though, the actual ground temperatures, as opposed to air temperatures, at the Phoenix site. They're given in Figure 2. From the graph it looks like the max ground temperature was around 255 K, or -18 C.

PHYSICAL AND THERMODYNAMICAL EVIDENCE FOR LIQUID WATER ON MARS?
Nilton O. Renno1, Brent J. Bos2, David Catling13, Benton C. Clark3, Line Drube4, David Fisher5, Walter Goetz6, Stubbe F. Hviid6, Horst Uwe Keller6, Jasper F. Kok1, Samuel P. Kounaves7, Kristoffer Leer4, Mark Lemmon8, Morten Bo Madsen4, Wojciech Markiewicz6, John Marshall9, Christopher McKay10, Manish Mehta, Miles Smith11, Peter H. Smith12, Carol Stoker10, Suzanne M. M. Young7.
1Department of Atmospheric, Oceanic, and Space Sciences, University of Michigan, Ann Arbor, MI 48103, 2NASA Goddard Space Flight Center, Greenbelt, MD 20771, 3Space Science Institute, Boulder, CO 80301, 4Niels Bohr Institute, University of Copenhagen, Copenhagen 302100, Denmark, 5Geological Survey of Canada, University of Ottawa, Ottawa K1A 0Y3, Canada, 6Max Planck Institute for Solar System Research, Max-Planck-Str. 2, Katlenburg-Lindau 37191, Germany, 7Department of Chemistry, Tufts University, Medford, MA02155, 8Texas A & M University, College Station, TX 77843, 9Carl Sagan Center, SETI Institute, Mountain View,CA 94043, 10NASA Ames Research Center, Mountain View, CA 94035, 11Jet Propulsion Laboratory, California Institute of Technology, Pasadena, CA 91109, 12Department of Planetary Sciences, University of Arizona, Tucson,AZ 85721, 13University of Washington, Seattle, WA 98195.
Introduction: The objective of the Phoenix Mars mission
is to determine if Mars’ polar region can support
life. Since liquid water is a basic ingredient for life as
we know it, an important goal of the mission is to determine
if liquid water exists at the landing site. It is
believed that a layer of soil preserves ice by forming a
barrier against high temperatures and sublimation, but
that exposed ice sublimates without the formation of
the liquid phase [1, 2]. Here we show independent
physical and thermodynamical evidence that besides
ice, liquid saline-water exists in areas disturbed by the
Phoenix lander. Moreover, we show that the thermodynamics
of freeze-thaw cycles ranging from diurnal
to geological time-scales leads to the formation of saline
solutions with freezing temperatures much higher
than current summer ground temperatures where surface
ice exists near the surface [3-4]. Thus, we hypothesize
that liquid saline-water is common on Mars.
This finding has important implications for the stability
of liquid water, weathering, mineralogy, geochemistry,
and the habitability of Mars.
...
Thus, TEut is ΔTEut ~ 70 K below the
freezing point even for single salts discovered at the
Phoenix landing site. Because of the large ΔTEut of
these salts, their eutectic solutions can form and remain
liquid almost anywhere on Mars. Since it has been
shown that even eutectic solutions of single salts with
modest freezing point depression such as NaCl (ΔTEut
~ 20 K) can sporadically be liquid almost anywhere on
Mars [5], we argue that liquid eutectic brines are common
on Mars.
...
Fig. 2 shows physical
evidence that various oblate spheroids observed on a
strut are liquid solutions that grow by deliquescence on
splashed material, likely a mixture of salts with large
amounts of perchlorate hydrates. Two spheroids, enclosed
by the white circle in Fig. 2, appear to have
merged with each other between martian days (Sols) 8
and 31. Most spheroids present substantial growth between
Sols 8 and 44, but not between Sols 44 and 90.
This suggests that the relative humidity reached a peak
value and the spheroids’ mid-afternoon salt concentration
became small enough for their saturation vapor
pressure to reach the atmospheric value, inhibiting
further growth during the later period.
http://www.lpi.usra.edu/meetings/lpsc2009/pdf/1440.pdf

Some of the co-authors here Catling, Clark, Lemmon and McKay count as among the most highly regarded of Mars scientists, so this is a major big deal. Intriguing also is that those white blobs on the landing struts are taken by them to be indications of liquid water.
However, if they are correct, the puzzling non detection of liquid by the TECP still needs to be explained.

Bob Clark