No he would be cold enough to get out obviously
after all he was in ice

If he was frozen when thrown into a lava, the ice will protect him until it's all gone, It will turn into steam creating a wall between him and the lava, the lava will then harden and create a barrier between him and the surrounding lava preventing his body to completely burn away. Unless he keeps sinking deeper and deeper, that obsidian shell won't melt. Since he didn't die from 1,000 years of being trapped inside an ice with no food or water, I doubt being baked inside an obsidian oven would make a difference.