You are fitting the function in the WRONG direction. This NOT a problem of fitting pressure as a function of temp difference. There is no functional relationship there.
The relationship that you have seems to be of the form tempdif(pressure). Thus as pressure changes, the temperature difference changes dependently.
But fine, you can still plot it with the variables on the axes you have chosen.
y = Tempdif;
x = Pres;
xq = linspace(min(x), max(x), 200);
pp = pchip(x, y);
yq = ppval(pp, xq);
plot(yq, xq, '-r',y, x, 'ob' )
xlabel 'Temperature difference (C)'
ylabel 'Pressure (nPa)'
You did make a good choice to use pchip instead of spline.