Adiabatic compression of air to 400 bar increases the absolute temperature by about a factor of 5.5, which would be the temperature of a flame.
400 bar is (from some quick searching) fairly mild for industrial hydraulic systems, and hydraulic fluid doesn’t get especially hot while in use.
On the other hand, a leak in a pressurized hydraulic system is extremely dangerous if you’re around it due to the extreme velocity of ejected fluid.