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Cut a continuous groove in the top and bottom pieces of the face frame and put a tenon on each vertical piece (using 1X lumber would be 1/4" groove and 1/4" tenon -- basically a rabbet on both sides of both ends of the verticals). Then cut 1/4" filler pieces to create the spacing between the verticals to put in the continuous groove so it's no longer a groove between them.
Don't know about the heat issue, however.
Edit: Tenon on each vertical is full width of the vertical. The whole face frame is easy work on a table saw. Something like this or that:
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I guess a having a portion of the top flip up to use a metal plate on the top of the radiator to keep a mug of hot chocolate warm would be out of the question?
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....working one's own wood......or working someone else's wood......?
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I reject your reality and substitute my own!
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I think they make those ugly perforated metal sheets like that so curious fingers don't go in and get burned. Keeping the top solid is fine. My parents had this type of cover in most rooms. All had solid tops. Never had a problem in 35+ years.
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No reason to fuss with a M&T joint for something like this... get a biscuit joiner.
Quick, easy, strong joints, no nails required.
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Maybe a rabbet rather than a butt joint for the vertical slats
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A biscuit joiner is perfect for this, but won't look as finished as a modified and ten on joint.
Do not use plywood. The edges will look terrible. Use solid wood. If you're going to paint it, use poplar.
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Depending on the thickness of the vertical slats, a dowel joint would work on anything 1/2" thick and above. You can get a dowel jig for 10 to 20 bucks, and you should also get dowel center transfer plugs for another few dollars to help you get perfectly aligned dowel joints.
As for the biscuit joiner, testing has shown that the biscuit joints are 1/4 as strong as a glued joint, and compared to tenons, pocket hole screws and dowels the biscuit joints fall far behind. Biscuit joiners are good for joining and aligning planks as the biscuits keep the boards in the same plane and the glue you put on the edges of the joined boards holds very well. Additionally, the inexpensive biscuit joiners cut slots that are not snug to the biscuits, further weakening the joint.
Hope this helps-
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Not being familiar with radiator heating, I can offer no advice.
But I will ask, why? Are they dangerous to the touch, do they burn? I honestly don't know.
If they aren't dangerous, they sure are charming to look at. To me, they appear to be functional antiques.
