It might not be the answer you are looking for, but I also commute about 3km and if it rains and isn't too cold I just take a change of clothes and a small towel and dry myself off and change when I get there. So instead of trying to keep dry I just accept that I'm going to get wet and take spare clothes. I'm lucky in that I can dry things off at work though.
Do you have mudguards on your bike
@Pearl? They make a big difference as water isn't getting sprayed all over you and the bike.
Has anyone used a cape? I'm put off by the idea that it might get very hot very quickly (especially in a climate like Thailand's, but also here) and if the wind is against you and you have a cape on I suppose it will be very difficult. But I believe they are unsurpassed when it comes to keeping you dry.