There was no difference between the air coming in to either side of the car. Also, I could feel the pipes leading to and from the matrix were hot, from the engine compartment side.
I decided to go for it and flush the matrix. Afterwards, I couldn't believe how hot it was! With the setting on 'HI' I cannot hold my hand against the vent for more than five seconds. Since I had a camera to hand, I took some pictures. I've posted them below.
Firstly, I had to remove the wipers and scuttle, as shown here:
http://www.omegaowners.com/forum/index.php?topic=111517.0Then I followed Jimbob's maintenance guide for flushing the matrix, as shown here:
http://www.omegaowners.com/forum/index.php?topic=90620.0The heater hoses look like this when they're attached and locked - you can see a coloured band:

When the outer sleeve is pulled back, it's unlocked and can be twisted and pulled away from the matrix metal pipes (I had to wrap it with a cloth to get a better grip):

There's not much space to get your hand in to twist and pull the hoses. I ended up with a few bruises.
To answer my own question, a tiny amount of coolant leaked out after pulling the top hose (less than 20ml), and no more than 100ml leaked out from the bottom hose.
Attaching a standard garden hose was the biggest and most time-consuming part of the whole exercise. Even with the ends softened with near-boiling water, it still took me about two hours to do this. One problem may have been that I was trying to do this with a stone-cold engine. As the matrix pipes were cold, the hose seemed to lose its flexibility as soon as I brought them together. If I was doing this again, I might try it with a warm (NOT HOT) engine. Anyway, here's what I ended up with:

As I'd read that I'd have to flush in both directions, I rigged up Hoselok connectors to make the job easier:

This is the pressure I set the water to for the first flush (basically to test the strength of the hose connections to the matrix pipes). I increased it once I was happy everything was going to hold together:

Here's the muck that was flushed out at the beginning of the first flush:

After about two minutes, the water ran clear. I then swapped the flushing direction. I continued to do this swapping-and-flushing about a dozen times. This picture shows the initial water quality after the eighth swap:

Once it flushed clean in both directions, I put everything back together. Job done!