I'm not an expert for sure, so have been reading and trying to sort it out. What I have read is that traditionally people have been too easy-peasy with radiators, putting newspapers on them, drying socks and gloves. Cotton ignites at 248F, which isn't much over the reference to radiators getting up to 212F. People used to use blankets to cover radiators and that was stated as a fire hazard.
I have spirited cats and my primary concern is for them to jump up on one or slide into one when running on the wood floors. I'm also concerned about radiator bursts and the spray, which would also be reduced somewhat by a cover.
I have to rent the lower end options and this apartment is actually beautiful with twice the square footage I currently have, so I would really like it, but am only concerned about the radiators. It has a door to the outside and no old, moldy cupboards like most cheap apartments.
I grew up in a house with radiators like those. We didn't have covers on them. My cat learned to avoid them, but would sometimes sit on the windowsill just above one - the window sills were about 8" higher than the top of the radiator. I used to put socks and sometimes my slippers on them to warm up, but never left them alone there. I don't recall ever seeing bursts or spray. Perhaps a different type of radiator would do that.
As for the covers: we didn't have any but I have seen them, like the one in your picture. They seemed to be made just of ordinary wood. I remember seeing metal covers, too, much in the manner of a fireplace screen but not a mesh, more a thin metal with holes and or slits, like this:
Yes, they got warm but nowhere near as hot as the radiator. I think the safety margin comes from: distance between the radiator and the wood - they are not supposed to be a close fit. Heat must then cross the air gap between radiator and cover. The extra distance also allows the top to be flush with the window sill as in the picture (assumes radiator is shorter by a handful of inches). Also the slats allow heat to escape, so the radiator can continue to do its job. You WANT the heat to transfer through and out. Preventing thermal transfer is what keeps the temperature inside the cover high, and the temperature of the wood. As heat is transferred to the cover, it will transfer again to the cooler room around. Mostly heat transfers to the air as it circulates through the slits/holes/gaps.
Bottom line: I would buy specifically designed covers if there is any way you can afford them. You could also build them, or buy one and copy for other radiators, but that requires having some hand tools and knowing how to use them, or having a handy friend who can help. If you have these resources, then that could save you some money.
Edit: If I recall right, some of the wooden ones were lined with thin metal to reflect heat away. Aluminum foil would do.
It looks a lot better with the cover.
