Can fresh hot asphalt damage slicks?
I don't think so - I've ridden over 1/4 mile stretches of freshly poured asphalt with no apparent damage to my tires. 

The asphalt is around 300 degrees F when it leaves the plant, but it will have cooled to 200 degrees or less by the time it's open to traffic (water will stand on the surface without boiling, so it's definitely below 212F)

Further, unless you're stopped, your tire has a very short contact period with the hot road. A typical road bike tire has a circumference of around 80 inches, and at 5mph, it will be rotating at about 1 revolution per second. If your contact patch is 2 inches long, that means each part of the tire is in contact with the hot road for only 2/80 = 25 milliseconds before having almost a second to cool off in the airflow. 25 milliseconds is about 1/10th the duration of a typical blink of the eye. Or, to look at it another way, each part of the tread only spends about 2.5% of the time in contact with the pavement and 97.5% of the time exposed to air.

The hot asphalt definitely has more "give" than cooled asphalt, so it will feel a bit spongy under your tires, but that's not because your tires are melting.

I'd be a little more worried about the fresh oils on the surface of the asphalt, the oil might degrade your tires if in contact for a long time, and it's super slippery if you hit a wet patch or ride over an iron plate before the oil wears off the tire's surface.