  The recent AvERA cosmological simulation of R\'acz et al. (2017) has a
$\Lambda \mathrm{CDM}$-like expansion history and removes the tension between
local and Planck (cosmic microwave background) Hubble constants. We contrast
the AvERA prediction of the integrated Sachs--Wolfe (ISW) effect with that of
$\Lambda \mathrm{CDM}$. The linear ISW effect is proportional to the derivative
of the growth function, thus it is sensitive to small differences in the
expansion histories of the respective models. We create simulated ISW maps
tracing the path of light-rays through the Millennium XXL cosmological
simulation, and perform theoretical calculations of the ISW power spectrum.
AvERA predicts a significantly higher ISW effect than $\Lambda \mathrm{CDM}$,
$A=1.93-5.29$ times larger depending on the $l$ index of the spherical power
spectrum, which could be utilized to definitively differentiate the models. We
also show that AvERA predicts an opposite-sign ISW effect in the redshift range
$z \approx 1.5 - 4.4$, in clear contrast with $\Lambda \mathrm{CDM}$. Finally,
we compare our ISW predictions with previous observations. While at present
these cannot distinguish between the two models due to large error bars, and
lack of internal consistency suggesting systematics, ISW probes from future
surveys will tightly constrain the models.
