4 awg wire too large for circuit breakers
I would go to 240V power instead of thick wire

First I would contact the manufacturer of the heater and see if they make a 240V version instead of 120V. Then I would run it as a 240V circuit instead of 120V, at what is typically half the amps. 

When you double the voltage and halve the amps, useful power is the same, but you reduce losses by a factor of 4.  Which means you can go down 6-8 sizes in wire on a long run like this.  Plug it into a voltage drop calculator and you'll see.