  We report on a densely time sampled polarimetric flux density monitoring of
the BL Lac object S5 0716+71 at 86 GHz and 229 GHz with the IRAM 30 m telescope
within a coordinated broad spectral band campaign, centred around an INTEGRAL
observation during November 10 to 16, 2003. Our aim was to search for
signatures of inverse-Compton "catastrophes". At 86 GHz, making use of a new
calibration strategy, we reach a relative rms accuracy of the flux density
measurements of 1.2%. At this frequency, S5 0716+71 showed no intra-day
variability, but showed remarkable inter-day variability with a flux density
increase of 34% during the first four observing days, which can not be
explained by source extrinsic causes. The 86 GHz linear polarization fraction
of S5 0716+71 was unusually large 15.0+-1.8%. Inter-day variability in linear
polarization at 86 GHz, with significance level >~95%; sigma_P/<P>=15% and
sigma_chi=6 deg., was also observed. From the emission variations at the
synchrotron turnover frequency (~86 GHz) we compute an apparent brightness
temperature T_B,app>1.4x10^14K at a redshift of 0.3, which exceeds by two
orders of magnitude the inverse-Compton limit. A relativistic correction for
T_B,app with a Doppler factor delta > 7.8 brings the observed brightness
temperature down to the inverse Compton limit. A more accurate lower limit of
delta > 14.0, is obtained from the comparison of the 86 GHz synchrotron flux
density and the upper limits for the synchrotron self-Compton flux density
obtained from the INTEGRAL observations. The relativistic beaming of the
emission by this high Doppler factor explains the non-detection of
"catastrophic" inverse-Compton avalanches by INTEGRAL.
