It may be a worry of yours but there are many people who use it as an option. It may be the highest cause of accidental fires, but I know a lot of people use them. I live in an old house, where my central heating system is just a big space heater attached to a wall in each room haha!
I'm not sure about blocking off the front of the rack. Will raise humidity due to lack of air flow, will get in the way and be a hassle, although minor. Have you checked for warmer spots in the room? Big rooms can have temp fluctuations in them of a few degrees. Maybe you could move the rack to one of these spots?