Audio Research VS110 Middle transformer gets very hot the 2 sides not so is this normal

That middle transformer is the power tranny. And all the incoming AC and current is going through it! So naturally it is going to heat up the longer your amp is in use! And if your speaker load tends to be 4 ohms or less, then that power tranny will get even hotter! The best solution is to replace it with a bigger transformer rated for more current. But a bigger transformer won't fit in that amp's chassis!

Poor design from Audio Research! Chassis and power tranny too small for rated power! 

Those Martin Logan electrostats have an impedance that falls to 1 ohm at high frequencies! A disaster for most tube amps. Try a big class A Krell or Pass amp instead!

Stop using that ARC amp when the power tranny starts getting hot! Otherwise you will end up with a dead transformer with melted windings (insulation)!

 Unless the middle transformer is getting really hot I would not worry. If you can touch the top you should be OK. The middle transformer is the power transformer for both channels while the other two transformers are channel specific. Notice how much bigger it is. You can email Audio Research and ask them if they think there is a problem for peace of mind.

  The SL3s are excellent speakers. The VS110 should have no problem driving them. I drove a pair of SL3s for years with a Classic 60 and then V70. I even had them for a short while with my current Ref 110. I finally replaced them with a pair of Sonus Faber Elipsa SE speakers.