Absolutely do not heel strike. It's not necessary, and you won't want to do it anyway because it will be painful.
When you run on clean asphalt with proper form, it should be quite comfortable and you generally should not get blisters or excessive wear on your feet. If you start with half a mile to a mile max barefoot in the first week and gradually increase the distance, your soles should adapt without problems.
The key to running barefoot on asphalt, or really any surface, without pain or blisters is correct form:
- Bend your knees
- Land lightly. Think of the lunar lander landing on the moon: begin to pull your feet up/back (by bending your knees) before they touch the ground, to lessen the impact
- Don't "strike" the ground but touch it. Focus on "lifting" your feet from the pavement rather than striking the pavement, this will help you be lighter on your feet
- Try to be very quiet on your feet. Quiet means low impact
The first part of the foot that should touch the ground is the ball of your foot. Followed quickly by your toes and then heel (or possibly heel then toes, whatever feels more comfortable). Yes, your heel can touch the ground, this helps the spring action of your calves to absorb shock and energy and propel you correctly, but it should barely touch the ground.
The way that your foot touches the ground -- ball-heel-toes -- allows the foot to spread out as it lands rather than after it's landed, so that you can distribute your weight over your foot without it sliding around. What causes blisters on pavement or other surfaces is the sliding or spreading of the foot over the surface. Visualize paint on your feet and try to leave perfect footprints. Proper foot alignment (toes straight forward and under your center of gravity, not too widely spread) and hip rotation will help here.
It's actually a great idea to start barefoot on asphalt, because asphalt will give your feet all sorts of feedback to encourage proper form. Once you can run comfortable barefoot on a hard surface, you can run on any surface barefoot (or in minimalist shoes).
Since it's easy to not notice pain, blisters, or other problems while running, a good way to prevent overdoing it, especially when you're starting out, is to stop every mile or so and rest for 30 seconds. Then evaluate and see if your feet feel fresh enough to continue. Otherwise you'll suddenly realize you should have turned back a while ago because your feet are too tender.