Should the tiles always be square? In that case, we need to have an options to force ticks separation equality for two axes (anyway, this is something I consider to implement).
Also, I suppose that the axes should have a discrete map for this plot type.

Aisde the ticks constraints, this should be easy to implement.

Might be time to consider this one. I'm still unsure about what should be done.

About the data,. I see three possibilities:
1. X values (n+1 values as a vector), Y values (m+1 values as a vector) and the data as an n*m matrix
2. X,Y and Z values as vectors, and optional bins for the X and Y limit values. The plot would display the mean of the Z values inside each cell
3. X and Y values as vectors, and optional bins, in that case the colors would represent the population (how many X,Y pairs in each cell).
4. other?

Which one(s) should I implement? I'm unsure also about the right plugin for that, might actually be a new one.

There are two aspects here:
-- there is the initial plot using the data as given. In this case (in the above link) the data originally arrives as 
#2 X,Y and Z values as vectors, and optional bins for the X and Y limit values.
The plot would display the mean of the Z values inside each cell
-- possible interpolation for grids (bin by bin pairs) that do not include any observations.

Note that your #1 (X values (n+1 values as a vector), Y values (m+1 values as a vector) and the data as an n*m matrix) seems to look to me like bug #657918.

Your #3 seems like a nice extension.

This problem has been fixed in our software repository. The fix will go into the next software release. Thank you for your bug report.