Heat maps in R with more than 2 categorical variables
Here is one way of visualizing the data you have presented. However, I have used some liberties and assumptions to create this plot. 

First, create a year_quarter variable that simply concatenates the year and quarter to present the time on the X axis. The following piece of code can do this in R

year_quarter = paste(dat$year, dat$Quarter, sep="-")


Now, the dataset you have will look like: 

&gt; dat


Variable  value year Quarter Location year_quarter
1        A 48.235 2011      Q1    North      2011-Q1
2        B 65.444 2011      Q2    North      2011-Q2
3        C 77.453 2011      Q3    North      2011-Q3
4        D 44.678 2011      Q4    North      2011-Q4
5        A 88.542 2012      Q1    South      2012-Q1
6        B 66.566 2012      Q2    South      2012-Q2
7        C 55.443 2012      Q3    South      2012-Q3
8        D 78.990 2012      Q4    South      2012-Q4 

Finally, using ggplto2, you can create the plot such that the colour represents the value, the shape represents the Location and the size represents the Variable. 

This simple one liner can help you produce such a plot:

p = ggplot(dat, aes(x = year_quarter, y = value, colour = value)) + geom_point(aes(shape = Location,size = Variable))

This is how the output plot looks like: 



Note that you can also add geom_line with interaction if you would like the lines to be connected based on Location and Variable.