Can I build storage in front of heaters?
If the radiators are still hot you'll have to get the shut offs repaired first. The heat and the resulting drying action will raise havoc with the wood. The issue isn't so much a fire hazard as a drying hazard. The wood is going to shrink in the winter and expand in the summer. The seams and joints will split. I would also make the design so that you have access to the radiator in the event of a leak.