  Recent simulation studies suggest that the compaction of star-forming
galaxies (SFGs) at high redshift might be a critical process, during which the
central bulge is being rapidly built, followed by quenching of the star
formation. To explore dust properties of SFGs with compact morphology, we
investigate the dependence of dust temperature, $T_{\rm{dust}}$, on their size
and star formation activity, using a sample of massive SFGs with $\log
(M_{\ast}/M_{\odot}) > 10$ at $1 < z < 3$, drawn from the 3D-{\it HST}/CANDELS
database in combination with deep {\it Herschel} observations. $T_{\rm{dust}}$
is derived via fitting the mid-to-far-infrared photometry with a mid-infrared
power law and a far-infrared modified blackbody. We find that both extended and
compact SFGs generally follow a similar $T_{\rm{dust}}-z$ evolutionary track as
that of the main-sequence galaxies. The compact SFGs seem to share similar dust
temperature with extended SFGs. Despite the frequent occurrence of AGNs in
compact SFGs, we do not observe any effect on dust caused by the presence of
AGN in these galaxies during the compaction. Our results disfavor different ISM
properties between compact and extended SFGs, suggesting that a rapid and
violet compaction process might be not necessary for the formation of compact
SFGs.
