Let's do a little math here.
Assumptions.
You cover the bed with a plastic box that is 6'x 3' x 4' high.
The R value of plastic is 1.
That you can put 6 1 gallon jugs of water inside for thermal mass.
We'll Ignore any other thermal mass in there such as the plants and ground.
That the water in the jugs starts at 70°F and can cool no further than 35°F
That you are trying to gain a 10° difference
The box has 90 square foot of area.
That means it loses 90 btu per hour per degree difference between inside and outside and that it will lose 900 btu/hour.
A gallon of water weight 8 lbs and it takes 1 btu to change a pound of water 1°F.
Therefore 8 x 6 x35 = 1680 BTU. That thermal mass will buy you around 1.5 hours with a large number of simplifications and assumptions.
I think once you start talking about adding thermal mass and such you are drifting more into a solar green house and away from a tunnel.
Covering it up with some kinf of insulation at night will definitely help. I'd do it about a houe BEFORE sunset.
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