Use a handheld stud finder to locate the studs within the wall. Mark the locations on the wall with a pencil. Find a stud on each side of the baseboard radiator. This is where the side boards of the wall frame will be anchored.
Screw two 2-by-4 boards the desired height of the cabinet to the side studs with 4-inch long wood screws and an electric screwdriver. Measure across the top of the radiator, including the side boards, and cut a 2-by-4 the same length with a saw. Screw the top board into the studs in the wall. The anchor frame is made.
Measure the outside of the anchor frame and cut 1-by-12-inch boards to fit the outside edge of the frame. Screw the corners of the boards together to form a three-sided rectangular frame. Attach this frame to the anchor frame with 2-inch wood screws.
Measure the rectangular area of the wall frame. Create a matching rectangle from 1-by-4-inch boards to build the front frame. Measure the empty space in the middle and cut a piece of decorative latticework 1 inch larger on each side. Staple the latticework to the back side of the front frame with an electric stapler.
Line up the edges of the front piece with the wall frame. Screw the front cover to the wall frame to complete an enclosed space. Secure a pre-made counter piece to the top of the cabinet that fits the measurements of the baseboard radiator cabinet. Smooth all exposed pieces with sandpaper. Paint the cabinet the desired color.