Under normal conditions, it will not burn, but each S1 draws close to 360watts, and should something go wrong, you do have a fire hazard on your hands. Acrylic or plexiglass both produce extremely toxic smoke when ignited, and once it starts to burn, as long as there is oxygen, it will continue to burn.
It's not something I would recommend.
Antminer S1 stock power consumption is 360W but on overclock its running on above 450W.
Even at that power consumption, the heat to top, and two side are very low, its cold air.
The hot air is only coming through the heatsink couple fins and goes out to the opposite side of the fan.
So, no hot air is actually hitting the covers. The cover is used to just redirect the cold air escaping through the sides and top back to the heatsink.
The above is from my practical experience. The fire can only come if you are over volting the miner or using non-standard PCI cables or Overloading PSU. Both of them need to be strictly avoided at any cost else the miner will get damaged in a matter minutes.