It's not clear from the abstract whether ice clouds still exist on mars or not. The small measured increase in solar irradiance includes UV so that it not likely to explain more than a small part of any earthly or martian warming. The unknown effect of changes in the sun's magnetic field, changes in electrons and other particles hitting mars could easily have warming effects different from earth's. I'm not ruling the sun in or out, just saying its unlikely that there's a direct solar irradiance effect responsible for warming on both planets.
The small measured increase in solar irradiance includes UV,
In fact most satellite instuments are only sensitive in relatively narrow bands generally focused on visual or IR and I know of no decadal studies of UV intensities over time, it is only very recently, we have even been able to do a credible job of measuring near UV out to 0.3microns.
More importantly the indirect effects of UV is not included in the studies I am aware of.
UV being much more energetic than visible and IR wavelengths and thus causing substantially greater changes in an atmosphere as regards ionization and effecting chemical decomposition and high energy reactions. The studies I have seen evaluate only direct themal heating effects as opposed to the much broader potential of high energy photons thus include a disclaimer similar to the article you reference to the effect that:
"Apart from solar brightness, more subtle influences on climate from cosmic rays or the Sun's ultraviolet radiation cannot be excluded, say the authors. However, these influences cannot be confirmed, they add, because physical models for such effects are still too poorly developed."
In fact the abstract of the original source paper makes it clear the study did not include any energetic UV effects:
Title: Variations in solar luminosity and their effect on the Earth's climate
Authors: Foukal, P.; Fröhlich, C.; Spruit, H.; Wigley, T. M. L.
Publication: Nature, Volume 443, Issue 7108, pp. 161-166 (2006).
Abstract
Variations in the Sun's total energy output (luminosity) are caused by changing dark (sunspot) and bright structures on the solar disk during the 11-year sunspot cycle. The variations measured from spacecraft since 1978 are too small to have contributed appreciably to accelerated global warming over the past 30 years. In this Review, we show that detailed analysis of these small output variations has greatly advanced our understanding of solar luminosity change, and this new understanding indicates that brightening of the Sun is unlikely to have had a significant influence on global warming since the seventeenth century. Additional climate forcing by changes in the Sun's output of ultraviolet light, and of magnetized plasmas, cannot be ruled out. The suggested mechanisms are, however, too complex to evaluate meaningfully at present.