Actually, yes, they do run very hot.
One thing to look at is the outlet you have the game plugged into. If it's a 15 or 20 Amp circuit, should be ok. If it's a 10 amp, and you have a few machines plugged into it, that might ask the machine to work a little harder.

I am by no means an expert, and may be wrong about that.

I'd say ad a GI fuse block, but I don't know if that will help the heat.

You can also switch the machine over to MOSFETs, which eliminate the heat entirely. Vid has a guide for upgrading driver boards on Williams Sys 3-7 (also works on 9).
If you like, switch out the feature lamps to run LED's. This will help your power consumption.

Others may have much better information.

Those resistors do get hot. Check out pinwiki for upgrading those resistors:

http://www.pinwiki.com/wiki/index.php?title=Williams_System_3_-_7#Controlled_Lamps_.28Lamp_Matrix.29

if you use a mosfet like FQP17P06 as the lamp column driver, the big current limiting resistors that get smoking hot are not needed and you can replace them with 1/4w resistors.

As the others have said, those resistors are part of the Lamp Matrix circuit and do get very hot. You have 2 options, both mentioned here already:

1) Replace them with new, higher wattage resistors
2) Replace the associated transistors with MOSFETs.

I use option 2 as it GREATLY reduces the heat produced by the board which lowers the temp in the backbox which is better for all the boards as well as the backglass, etc.

I use IRF9Z34N to the column drive (the transistors next to the burned resistors).
I use IRFZ34N for the row drive.

If you use MOSFETS, you can replace the burned resistors with jumper wires or zero ohm resistors

I think you still want to have a current limiting resistor in there. At least in some kind of "oh shit" situation a limiting resistor might burn itself open instead of burning something else.

Use a 1/4w resistor in a low ohm range. Like 22-270 ohm.

That is because I typoed the part number DOH! Its actually a IRF9Z34N (I fixed my earlier post).