I've used Lizard Skin in the past for both sound and heat and it worked great. On the XK, I'd focus on the trunk.

 

I did a home brew lizard skin. It was great for heat but not so great for sound control. I did roofing tar and wax paper on my truck. made one heck of a mess but the floor is quiet and I doubt it'll ever rust out. Lizard skin was microscopic glass bubbles and white rubberized roofing paint sprayed with an undercoat gun. It actually turned out really good.

 

I applied both. the heat control along the firewall and trans tunnel and the roof. Sound control in the doors, trunk, wheel wells and underbody.

This was an 86 MY so the glass limited sound control but it improved both.