Cluster data in heat map in R ggplot

You can achieve this by defining the order of Timepoints in a dendrogram after you have applied hclust to your data:

data <- scale(t(data))
ord <- hclust( dist(data, method = "euclidean"), method = "ward.D" )$order
ord
[1]  2  3  1  4  8  5  6 10  7  9

The only thing you have to do then is transforming your Time-column to a factor where the factor levels are ordered by ord:

pd <- as.data.frame( data )
pd$Time <- sub("_.*", "", rownames(pd))
pd.m <- melt( pd, id.vars = "Time", variable.name = "Gene" )

pd.m$Gene <- factor( pd.m$Gene, levels = colnames(data), labels = seq_along( colnames(data) ) )
pd.m$Time <- factor( pd.m$Time, levels = rownames(data)[ord],  labels = c("0h", "0.25h", "0.5h","1h","2h","3h","6h","12h","24h","48h") )

The rest is done by ggplot automatically:

ggplot( pd.m, aes(Time, Gene) ) +
  geom_tile(aes(fill = value)) +
  scale_fill_gradient2(low=muted("blue"), high=muted("red"))

I don't think ggplot supports this out of the box, but you can use heatmap:

 heatmap(
   as.matrix(dat), Rowv=NA,
   Colv=as.dendrogram(hclust(dist(t(as.matrix(dat)))))
 )

Note this won't look like yours because I'm just using the head of your data, not the whole thing.

Here we specify the clustering manually with a dendogram derived from your hclust with the Colv argument. You can specify the clustering manually too through the Colv argument if the one used by default doesn't line up with what you want.