Just a couple more things to really nail it.
 
Not only does lead have a low melting point, it has a low specific heat of 0.13 kJ/kg.degree. All this means is that it heats up quickly. However the only energy available to do this heating is the kinetic energy imparted during the throw so any energy converted to heat means speed loss and consequent loss of carry distance. But even so if all the kinetic energy in a gland thrown at 50 m/s were somehow to be converted to heat it would raise its temperature less than 10 degrees.
 
Also this supposition totally ignores the fact that at slinging type speeds the passing air would be a cooling factor not a heating one. Any thrown hot missile is going to arrive at the target colder than it started, not hotter. Sure meteorites burn up in the atmosphere but their speeds are thousands of times faster than those of sling bullets; the analogy doesn't hold.
 
The only time where heating sling ammunition may be of some effect is when hot stones were thrown onto thatched rooves with the aim of igniting them. I admit I've never done any experimentation with this but even this sounds pretty farfetched. I just can't see a stone being heated hot enough to ignite straw after having flown through cooling air for 100m or so. It might work with a large iron missile which can be heated far hotter than lead.
 

The heated stone thing was done for a TV program about conquistadors. A folded bit of cotton protected the sling pouch and was replaced for each shot.

Quote from David Morningstar on Mar 7^th, 2011, 3:06am:
Yes indeed I read it somewhere on the forum that cotton soaked in pitch? was wrapped around the heated shot and when slung it would burst into flames.It sound good and realistic,the hard part would be that somehow the cotton must be tied to the stone really good,and the hot stone would probably make the pitch smoke and ignite quickly I think.I know that you wrote about another version when you place a piece of cotton on the pouch as a "sabot" so the hot stone doesn't ignite the pouch.If you know a link about that TV show,could you post it ?I've looked after it but found other shows.If you can't find the link ,the name of the show would help too.

There were probably two reasons that ancient peoples though sling bullets melted in flight. One, lead deforms a lot when it hits something and looks like a motion capture image of a splash of liquid. Two, the lead does heat up a little during flight from friction and on impact from adiabatic heating. Together they make it seem like the lead heated and melted in flight, but cooled off after hitting the target.

I had a batch of clay glandes in the kiln that I wanted to cool quickly, they were too hot to touch but not as hot as when I fired them, I dropped them in the dog water bucket.  They hissed as they hit the water and made some small bubbles but seemed to cool quickly.  I picked one out, it was wet but rapidly evaporated the water and pretty quickly got too hot to hold comfortably.  I think that if you heated it red hot and wrapped it in something to protect the sling, it would still be hot enough to start a fire when it got there.  Bill

I think clay would be much better for starting fires than lead because clay and ceramics hold heat for longer than metals can.

I think I have a lead sinker or two that could be improvised fire starters. I just have to make sure I have enough to equal a glans. The 4th of July is coming up, and it is traditional to light fires (or fireworks)...

Also keep in mind that specific heat is measured in heat/mass, and lead is very dense, comparing heat/volume between lead and clay might be interesting, however, you could heat clay much hotter than lead due to its low melting point.