We present space-based thermal infrared observations of the presumably Geminid-associated asteroids: (3200) Phaethon, 2005 UD, and 1999 YC using Wide-field Infrared Survey Explorer/Near-Earth Object WISE. The images were taken at the four wavelength bands 3.4 μm (W1), 4.6 μm (W2), 12 μm (W3), and 22 μm (W4). We find no evidence of lasting mass loss in the asteroids over the decadal multiepoch data sets. We set an upper limit to the mass-loss rate in dust of Q
dust ≲ 2 kg s−1 for Phaethon and ≲0.1 kg s−1 for both 2005 UD and 1999 YC, respectively, with little dependency over the observed heliocentric distances of R
h = 1.0–2.3 au. For Phaethon, even if the maximum mass loss was sustained over the 1000(s) yr dynamical age of the Geminid stream, it is more than two orders of magnitude too small to supply the reported stream mass (1013–14 kg). The Phaethon-associated dust trail (Geminid stream) is not detected at R
h = 2.3 au, corresponding to an upper limit on the optical depth of τ < 7 × 10−9. Additionally, no comoving asteroids with radii r
e < 650 m were found. The DESTINY+ dust analyzer would be capable of detecting several of the 10 μm sized interplanetary dust particles when at far distances (≳50,000 km) from Phaethon. From 2005 UD, if the mass-loss rate lasted over the 10,000 yr dynamical age of the Daytime Sextantid meteoroid stream, the mass of the stream would be ∼1010 kg. The 1999 YC images showed neither the related dust trail (the optical depth τ < 2 × 10−8) nor comoving objects with radii r
e < 170 m at R
h = 1.6 au. Estimated physical parameters from these limits do not explain the production mechanism of the Geminid meteoroid stream. Lastly, to explore the origin of the Geminids, we discuss the implications for our data in relation to the possibly sodium-driven perihelion activity of Phaethon.