Will the Mini Ice Age solve our Global Warming Heat problem
I'm going to try to answer this, though it's actually a very hard question depending on how close you look at it.    

Lets start with the American Physical Society's statement on climate change - which, they've made an effort to balance out following their 2007 statement of "evidence is incontrovertible" that got some members upset and lead to a handful of high profile resignations.    More on that here

This is their more balanced statement.

http://www.aps.org/policy/reports/popa-reports/energy/climate.cfm


  The relationships between the atmospheric concentration of greenhouse
  gases and their radiative effects are well quantified. Forcing from
  the long-lived greenhouse gases: carbon dioxide, methane, and nitrous
  oxide, is presently about 2.5 Watts per meter squared (W/m2). Of this
  total, 1.6 W/m2 is from carbon dioxide alone. The total anthropogenic
  forcing is uncertain, particularly because the magnitude of the
  negative forcing associated with sulfate aerosols is unclear. While
  changes in solar irradiance may have affected global climate in the
  last century, a 0.15% change irradiance, the order of estimated
  changes, results in only a 0.36 W/m2 forcing.


and, numbers vary, but this seemed a pretty fair article on Solar Irradiance:   http://earthobservatory.nasa.gov/Features/SORCE/sorce_03.php

It says:   


  The number of sunspots visible from the Earth not only changes from
  day to day, but also in cycles that can last from decades to centuries
  to millennia. The most well-known and well-analyzed of these cycles is
  the 11-year sunspot cycle. Over the course of 11 years, the yearly
  average number of sunspots and faculae slowly increases and then
  return to normal levels before rising again for the subsequent cycle.
  The change in the Sun’s yearly average total irradiance during an
  11-year cycle is on the order of 0.1 percent or 1.4 watts per square
  meter.


So, 1.6 watts per square meter from Co2 (2.5 watts total) and (up to) 1.4 watts per square meter low to peak solar irradiance, but there's a problem with that 1.4 number.    It's low to high, meaning low to average is 0.7 watts per square meter and that's how we should measure assuming the sun enters a grand minimum, we should measure against the average, so the real number is 0.7 watts per square meter drop - assuming the study is right and the sun does enter a new Maunder Minimum.

Skeptical Science posts a similar number:   



Source:  https://www.skepticalscience.com/solar-activity-sunspots-global-warming.htm

The variation in their chart appears to be similar to the 0.7 variation we should expect from the NASA article, average to low range.

There's also the, all but guarantee that CO2 will continue to rise, at least, for several more years, so the APS estimate is likely to go up.   Also, the APS number doesn't include feedback mechanisms - and they say as much in the article linked above:


  The largest source of uncertainty lies in determining the magnitude of
  climate feedbacks. For example, an increase in trapped radiation and
  the associated warming is expected to increase the level of water
  vapor in the atmosphere, which would tend to further enhance the
  greenhouse effect ó a positive feedback. An example of a negative
  feedback would be an increase in clouds that reflected more sunlight
  back into space. The actual feedback from changes in clouds is
  uncertain since they also act to trap outgoing infrared radiation.


Now, the positive feedback from water vapor is a given and the negative feedback from clouds is more uncertain, so I think the APS article is a little bit more friendly to the skeptics than the actual science (IMHO).  Clouds reflect sunlight, but clouds also trap heat at night.  The total cloud effect is, well, a little more cloudy than APS' one line suggests.

Skeptical Science has an article on cloud feedback here:  http://www.skepticalscience.com/clouds-negative-feedback.htm

So, where does that leave us:

Well, first, the study that the sun is going to enter a grand minimum in the next few decades needs to be verified, lets start there.   A whole bunch of bad science has been published by those trying to disprove, discredit or cast doubt on climate change - so skeptisism of new studies first, especially on this topic, but, lets say they're right - which was the original question.   Would that be sufficient to stop man made global warming?

No.   I think it's pretty likely it would be insufficient.   0.7 is less than 2.5.   But, if they're right, it's still kind of good news, cause it would soften the blow - and that's a good thing.   I hope they are right.   But the sun's maximums and minimums have a pretty small effect on climate change.  Maybe a degree here or there.   Man made climate change should be 2 degrees by the end of the century, and perhaps more if left unaddressed in centuries that follow.

As Steve Emmerson points out, the effect of the Maunder Minimum isn't 100% accepted as the sole cause of the Mini ice age.   There's still some unknowns, but I feel, with pretty high confidence, that the sun entering a new grand minimum would be insufficient to stop the warming, but it might slow it down, a little.

Too long?   I can try to clean it up a bit later.