Creating a likelihood heatmap given many pairs of x and y values of different lengths?

So I have generated a bunch of data curves (like thousands), say temperature with depth. so have say 1000 arrays of depths and 100 corresponding arrays of temperature (n.b. they are not all the same length)

What I want to do is create a heatmap where the color corresponds to how often one of these data curves had that value at that depth. i.e. how many curves pass through that particular bin.

Could anyone offer advice on how to do this?