There are four items to throw into the fire:
A gold bar from the top shelf on the left as you enter the room
A lava-lamp-shaped item from the back left corner of the room
A valve wheel from the bottom shelf on the right side of the room
A gear from the top shelf of the table in the near right corner (the same shelf with the radio)
The radio does not need to go into the fire for this achievement.
I got on the shelves by simply climbing up the shorter shelves and wall climbing over to the shelves with the items, but you can also use the tall boxes that come out of the chutes to create extra platforms, if you don't like to climb along the walls.
Quoting
planchetflaw 's comment: Grab the first and go left and hold it against the wall between the gold bar shelf and the climbable one. It will magnetised in place. Then continue doing that for the munitions (2 blocks), and then finalltly 3 blocks for the cog.
It's actually simple using those blocks and requires no proper platforming aside from simple jump grabs.