first thing, close the damper on the baseboard unit, that will cut down the
convection currents..
stuff the bottom of the baseboard with something to stop it, as was previously
suggested...
cut the aluminum fins off the copper pipe, carefully, then insulate....
the temperature of the water is never going to be above about 180 degrees,
farenheit, so don't worry about the insulation melting....
but have you considered moving the bed?