There are quite a few different colormaps, and you can make your own custom colormap too. Use doc colormap to see them in more detail:

If you are using the HSV colormap and only seeing blue to red colours then it is because your colour axis limits are such that only that part of the colormap is being sampled. So if your data spans from 0.5 to 1.0 but you set the colour axis to caxis([0.0 1.0]) then you would only see half of the colours in the colormap.

In order to get a colormap like you describe, you can use this approach where you specify the minimum and maximum colours and create a colormap that blends from one to the other. Note that you will have to set your colour axis values according to the limits of your plot appropriately (commands like surf automatically stretch to include all the colours).

% number of map indices
Nmap = 64;

% colormap from cyan to red
cMin1 = [0 1 1];
cMax1 = [1 0 0];
cMap1 = zeros(Nmap,3);
for i = 1:Nmap;
    cMap1(i,:) = cMin1*(Nmap - i)/(Nmap - 1) + cMax1*(i - 1)/(Nmap - 1);
end

% colormap from white to red
cMin2 = [1 1 1];
cMax2 = [1 0 0];
cMap2 = zeros(Nmap,3);
for i = 1:Nmap;
    cMap2(i,:) = cMin2*(Nmap - i)/(Nmap - 1) + cMax2*(i - 1)/(Nmap - 1);
end

% make up some data
Z = linspace(0,1,100)'*ones(1,100);

% plot with HSV colormap
figure
surf(Z,'edgealpha',0);
colormap('hsv');

% plot with cyan-to-red colormap
figure
surf(Z,'edgealpha',0);
colormap(cMap1);

% plot with white-to-red colormap
figure
surf(Z,'edgealpha',0);
colormap(cMap2);

Which should produce:

I believe that caxis is the command you're looking for. Usage:

caxis([minValue maxValue]) 

Using caxis like this, all values outside the range [minValue maxValue] will be coloured with the lowest or highest value in the colormap, respectively.

Since colorbar and friends use colormap, you'll have to adjust the current colormap if you want to adjust the number of colors used. Do this like so:

%# get current colormap
map = colormap;  

%# adjust for number of colors you want
rows = uint16(linspace(1, size(map,1), NUM_COLORS)) ;
map = map(rows, :);

%# and apply the new colormap
colormap(map);

Of course, combining this with caxis is the most powerful.

If you don't want to show some values outside of range, that's not a job for colorbar or caxis, that's up to you -- you'll have to adjust the data that's plotted so that all values you don't want plotted are NaN. Doing so will make Matlab understand that you don't want to plot these data:

data( indices_to_data_not_to_plot )  = NaN;
surf(x,y,data);  %# or whatever you're using

I think all that you're missing is a call to caxis to specify the minimum and maximum values to map the color range to:

caxis([18 23]);

Note that the following line...

cb.Limits = [18 23];

... only changes the tick limits displayed on the colorbar, but doesn't change anything about how the data is mapped to the color range. The caxis function is how you control that (in the above case, mapping the value of 18 to one end and the value of 23 to the other). By default, your code was mapping the minimum and maximum values in Z to the color range (20.5 and 23, respectively). When you then set the tick limits on the color bar to a larger range, it just filled it in with the last color in the color map, in this case red. That's why you see so much of it.

Bonus

Just because you might be interested, you could also use interpolation via the interp1 function to easily generate your color map like so:

cmap = interp1([1 0 0; 1 1 0; 0 1 0], linspace(1, 3, 41));