We report on coordinated thermal and optical measurements of trans-Neptunian object ( 20000 ) Varuna obtained in January-February 2002 , respectively from the IRAM 30-m and IAA 1.5 m telescopes . The optical data show a lightcurve with a period of 3.176 \pm 0.010 hr , a mean V magnitude of 20.37 \pm 0.08 and a 0.42 \pm 0.01 magnitude amplitude . They also tentatively indicate that the lightcurve is asymmetric and double-peaked . The thermal observations indicate a 1.12 \pm 0.41 mJy flux , averaged over the object ’ s rotation . Combining the two datasets , we infer that Varuna has a mean 1060 ^ { +180 } _ { -220 } km diameter and a mean 0.038 ^ { +0.022 } _ { -0.010 } V geometric albedo , in general agreement with an earlier determination using the same technique .