I'm looking at your avatar and I'll proceed as if that's the cooker we're talking about. (I was assuming yours was a fully vertical unit, as is mine, in which the charcoal box is directly under the meat racks--bad to ASSume. )
And if your problem is more one of temps running too cool instead of too much fluctuation (another potential misunderstanding on my part) I think I have a simple fix....
Ensure your basket (which is quite nice btw) is not sitting flat on the bottom of your side-mounted smoke box. The fire must be able to pull in air from underneath. If nothing else, just find 4 smooth, similarly sized rocks for that basket to sit on. I'm assuming the inlet from the fire box into the cook box will still then be above the level of the coals in the basket...you simply must not block off the path of the smoke into the cook chamber.
Also you need at least 1/4" gap between the right side of the basket to the air inlet hole in the fire box to the outside world. The basket can be shoved up to the wall on the left but you need a gap on the right for the air to come in and go under the basket to where the fire is in the maze. Trust me, once the fire is going, the vacuum pulling the air down under the basket will be a lower resistance path than to go straight across from firebox from inlet to cook chamber, even if that's geometrically a shorter path.
Maybe most importantly, I highly recommend you start your fire in the front left of your maze. I use one of those round electrical starter elements for ~10 mins then once you see several coals burning, you pull it out, push your basket in, and close the door. But however you like to start a fire should work just fine. But you want the fire to work it's way in your maze toward the fresh air so start it on the LEFT. That way any ash that drops down underneath does not block the airpath for where the fire is headed.
Finally, if you still can't get enough heat, or your fire goes out going around corners, you need more air. You can drill an array of small holes in the bottom of your side smoke box as I did. (Have a catch pan underneath for hot coals to fall into, not on the floor.) Or for starters, I'd recommend a fan outside the factory inlet. A 120VAC pump for blowing up large air mattresses works well for this. To reduce the flow into the firebox (and you only a little extra flow) just pull the fan away from the opening so a smaller fraction of the forced air enters the firebox. (You'll want your fan on a box or stand so you can properly aim it at the inlet hole.)
If some day you want to get really fancy, you can put a feedback loop on the fan speed so that as your cooking temperature goes high, the fan is slowed down, and vice-versa. But let's get you walking before you run.
Let us know how it goes. Try a $1 package of hot dogs so you won't feel bad if this takes a couple iterations.
