How to extract correlation of fixed effects on lmer output

If you have a multi-level model with many factors and interactions, the correlation size of the matrix of fixed effects can become quite large and unclear.

I can use the parameter symbolic.cor=Tin the print method to make a clearer printout of the summary, as shown below:

ratbrain <-
within(read.delim("http://www-personal.umich.edu/~bwest/rat_brain.dat"),
{
treatment <- factor(treatment,
labels = c("Basal", "Carbachol"))
region <- factor(region,
labels = c("BST", "LS", "VDB"))
})

print(mod<-lmer(activate ~ region * treatment + (0 + treatment | animal),ratbrain),symbolic.cor=T)

Here is a slightly clearer correlation matrix for large matrices. Although this matrix of examples is not so big. But it would be nice if I could draw a heat map of the correlations.
How to extract the correlation of fixed effects so that I can make this heat map?

EDIT:

Here is the function that I created thanks to the answers.

fixeff.plotcorr<-function(mod,...)
{
  #require(GGally) # contains another correlation plot using ggplot2
  require(lme4)

  fixNames<-names(fixef(mod))

  # Simon O'Hanlon answer:
  # so <- summary(mod)
  # df<-as.matrix(so@vcov@factors$correlation) for version lme4<1.0
  # df<-as.matrix(so$vcov@factors$correlation)  # lme4 >= 1.0

  df<-as.matrix(cov2cor(vcov(mod))) #Ben Bolker solution

  rownames(df)<-fixNames
  colnames(df)<-abbreviate(fixNames, minlength = 11)

  colsc=c(rgb(241, 54, 23, maxColorValue=255), 'white', rgb(0, 61, 104, maxColorValue=255))
  colramp = colorRampPalette(colsc, space='Lab')
  colors = colramp(100)
  cols=colors[((df + 1)/2) * 100]
  # I'm using function my.plotcorr which you can download here:
  # http://hlplab.wordpress.com/2012/03/20/correlation-plot-matrices-using-the-ellipse-library/
  my.plotcorr(df, col=cols, diag='none', upper.panel="number", mar=c(0,0.1,0,0),...)

  # Another possibility is the corrplot package:
  # cols <- colorRampPalette(c("#67001F", "#B2182B", "#D6604D", "#F4A582", "#FDDBC7", 
  #                              "#FFFFFF", "#D1E5F0", "#92C5DE", "#4393C3", "#2166AC", "#053061"))
  # require(corrplot,quiet=T)
  # corrplot(df, type="upper", method="number", tl.pos='tl', tl.col='black', tl.cex=0.8, cl.pos='n', col=cols(50))
  # corrplot(df,add=TRUE,  method='ellipse', type='lower', tl.pos='n', tl.col='black', cl.pos='n', col=cols(50), diag=FALSE)
}

my.plotcorr . fixeff.plotcorr(mod) :