The cooling is going to draw that kind of wattage because the 'smoke eliminator' element is burning away too to kill the smoke coming out. otherwise its just the fan and motor running.
I work for a power plant and can tell you that voltages can vary significantly from time of day, temperature, and even in your building depending on what you have on.
I can be supplying 125 volts to your weatherhead, but if your A/C is running, you got the coffee thing cooking, possibly cooking dinner, and maybe even the water heater and washer / dryer... guess what, your voltage house wide is going to be quite low. Nature of the beast there.
The age of the wiring in your house plays a big part, if you have aluminum wire plays a huge and most the times dangerous part....
Also, you plug the thing into a plug which is basically two pieces of brass that are springy together, so it's a pressure contact point, not really a hard contact, like bolted on or wire nutted or something difinitively making good solid contact. Over time that plug can corrode, or the springiness gets weak and the connection is not very good, its loose, voltage loss will happen there.... The kill a watt's I have one for a certain type of..... cooker i use, and the plugs in them are not the very best either, I burnt up more than one kill a watt on a mere thousand watts running through it for a few hours because of the loose springy plug thing. yep voltage loss there, almost 3 volts.
Yes the variac can correct the voltage at the cooker but it does not correct the problem... you get the higher voltage at the cost of extra amps... if your circuit is overloaded, or you have loose contacts causing poor connection and HEAT at that spot, pulling more amps through it is only going to make that problem worse. Before you go this route, please take a look and see if you can see what is causing the low voltage first, and be sure it's not a fault that could potentially turn into a fire.
Aaron