MATLAB interpolation wrongly extrapolates over concave boundary

Question

I want to plot my surface solutions from Ansys Fluent in a contourf plot with MATLAB. The solution is a table in ASCII format with scattered points (x,y,z) which describe a plane and a temperature at each of those points.

On the first picture you can see a scatter plot with all points and temperature as color. Here you can see the correct geometry of the boundary.

But if I want a contour plot, I need to interpolate the scattered points. On the next picture you can see the result. The problem is that MATLAB interpolates "through" the boundary, for example at the bottom. I think the problem has something to do with the concave boundary and the Delauney triangulation.

My code

clear all
close all
clc

data_txt = importdata('file'); % 5Columns: NodeNumber, x,y,z,temperature

data_int = scatteredInterpolant(data_txt.data(:,3),data_txt.data(:,4),data_txt.data(:,5),'natural','none');

x_min=min(data_txt.data(:,2));
x_max=max(data_txt.data(:,2));

y_min=min(data_txt.data(:,3));
y_max=max(data_txt.data(:,3));

z_min=min(data_txt.data(:,4));
z_max=max(data_txt.data(:,4));

x = x_min:0.0001:x_max;
y = y_min:0.0001:y_max;
z = z_min:0.0001:z_max;

[Y, Z] = meshgrid(y, z);

data_int_ = data_int(Y,Z);

figure_handle=figure;
contourf(Y,Z,data_int_,100,'Edgecolor','none');

In this case, the x-Coordinate is constant. I can do this with every coordinate by using a rotation matrix. Than I have a x,y,data problem.

Is there a way to interpolate my scattered points, but to get the correct boundary shape? How can I stop Matlab from interpolating concave regions with no data?