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

What are your speakers?  How loud are you pushing it?

Martin Logan sl 3
just loud enough to here all the music 
about 9 o’clock on pre amp which starts out at 7 o’clock 

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!