  The bright submillimetre (sub-mm) galaxy MM 18423+5938 at redshift 3.9296 has
been predicted from mid-infrared and millimetre photometry to have an
exceptionally large total infrared (IR) luminosity. We present new radio
imaging at 1.4 GHz with the Westerbork Synthesis Radio Telescope that is used
to determine a radio-derived total IR luminosity for MM 18423+5938 via the well
established radio-far-infrared correlation. The flux density is found to be
S_1.4 GHz = 217 +/- 37 \mu Jy, which corresponds to a rest-frame luminosity
density of L_1.4 GHz = 2.32 +/- 0.40 x 10^25 / u W / Hz, where u is the
magnification from a probable gravitational lens. The radio-derived total IR
luminosity and star-formation rate are L_8-1000 \mu m = 5.6^+4.1_-2.4 x 10^13 /
u L_sol and SFR = 9.4^+7.4_-4.9 x 10^3 / u M_sol / yr, respectively, which are
~9 times smaller than those previously reported. These differences are
attributed to the IR spectral energy distribution of MM 18423+5938 being poorly
constrained by the limited number of reliable photometric data that are
currently available, and from a previous misidentification of the object at 70
\mu m. Using the radio derived total IR luminosity as a constraint, the
temperature of the cold dust component is found to be T ~ 24^+7_-5 K for a dust
emissivity of \beta = 1.5 +/- 0.5. The radio-derived properties of this galaxy
are still large given the low excitation temperature implied by the CO emission
lines and the temperature of the cold dust. Therefore, we conclude that MM
18423+5938 is probably gravitationally lensed.
