  We give an explanation for the origin of various properties observed in local
infrared galaxies, and make predictions for galaxy counts and cosmic background
radiation (CBR), by a new model extended from that for optical/near-infrared
galaxies. Important new characteristics of this study are that (1) mass scale
dependence of dust extinction is introduced based on the size-luminosity
relation of optical galaxies, and that (2) the big grain dust temperature
T_dust is calculated based on a physical consideration for energy balance,
rather than using the empirical relation between T_dust and total infrared
luminosity L_IR found in local galaxies, which has been employed in most of
previous works. Consequently, the local properties of infrared galaxies, i.e.,
optical/infrared luminosity ratios, L_IR-T_dust correlation, and infrared
luminosity function are outputs predicted by the model. Our model indeed
reproduces these local properties reasonably well. We then found considerably
different results for MIR-submm counts and CBR from most of previous works
based on the empirical L_IR-T_dust relation; especially, it is shown that the
dust temperature of starbursting primordial elliptical galaxies is expected to
be very high (40-80K). This indicates that intense starbursts of forming
elliptical galaxies should have occurred at z~2-3, in contrast to the previous
results that significant starbursts beyond z~1 tend to overproduce the
far-infrared (FIR) CBR detected by COBE/FIRAS. On the other hand, our model
predicts that the mid-infrared (MIR) flux from warm/nonequilibrium dust is
relatively weak in such galaxies making FIR CBR, and this effect reconciles the
prima facie conflict between the upper limit on MIR CBR from TeV gamma-ray
observations and the COBE detections of FIR CBR. (abridged)
