I cycle daily (five days a week) to and from work. It is not far, 9 km each way, and takes me 20-25 minutes, depending on direction and intensity.
If I cycle with full intensity, my legs are quite heavy on fridays. If I cycle with moderate intensity my legs are fine, even on fridays.
My goals for cycling are loosing weight (of course combined with a diet) and general well-being.
At what intensity would you recommend me to cycle?
Well I'd recommend you to cycle the way you feel most comfortable with. I would recommend you to cycle at an average pace to work and decide daily how you want to cycle back. Maybe you need to relieve some stress or aggression, so just bite your handlebar and go full speed. Maybe you are exhausted already anyway, so just keep it slow.
Cycling 18km daily will of course have a positive effect on your body, but it wont do magic, changing your diet will probably have the bigger effect.
Just to give you a rough idea. I commute about 14km every day (8 miles). My average speed measured over several month is 21.5km/h. This includes riding through city traffic and stopping at traffic lights all the time.
Usually if the road is free my speed is around 25-30 km/h. I live in a pretty flat area and the elevation on my commute is not more than 60m (according to GPS).
Cycling the first week after my holidays was horrible - no stamina whatsoever and I was significantly slower.
Bottom line: Cycle as fast as you can, it looks like you are doing a good commuting pace already but listen to your body and slow down if you feel tired.
To loose weight you have to elevate your heart rate (elevate means not max. out) and a bit of muscle fatigue is maybe part of every serious exercise and is nothing bad at all.
I sometimes like to sprint between traffic lights just to mix up the exercise and to build more muscle from pushing harder. Some stretching after cycling can also do wonders.
The most important is that you enjoy it!
I'm going to disagree with the answer provided even though it is mostly factually correct.
I think you should try and maintain as high a pace as you can during your commute, while staying in you aerobic range. The easiest way to find the correct pace is to wear a heart rate monitor while riding and target a particular HR Zone (read-up on heart rate training zones first here or there). Make allowance for the availability of showers at work, otherwise your co-workers will not like your sweaty arrivals much.
The thing is your legs might hurt on Fridays right now, but give it a few weeks or months, and you'll be able to do this really easily with no residual soreness. As you get faster on your bike with repetition, you should start taking little detours in order to keep you commute above 20 or 25 minutes duration. If you can fit 40 to 60 minutes of medium to high intensity cardio in you daily schedule that way, I believe you will see significant results.
If you want to loose weight, you should do intervals. Go all out for 20-30 seconds, than go slow for 30-60 seconds. Repeat this 5-10 times, depending on your energy expenditure.
High Interval training is by far the most effective way to loose weight - except eating clean off course.
