OK...here are the simple mods you can make to most "cheap" off-sets.......
Your exhaust vent needs to be extended down to the grate level....it is currently fixed at the top of the unit. This can be done easily with some aluminum flashing....just roll it up and shove it up into the exhaust pipe and make sure it comes all the way down to the grate. It makes opening the top a little more difficult on some models, but you need this to be done.
Why??? Heat will follow the path to the nearest exhaust opening. In this case it goes directly from your firebox, thru the opening and directly up to the top of the unit. Thereby passing OVER your meat. The temp difference between the grate and the top of the unit can be 100º! By getting that exhaust opening at the grate....the heat will now flow horizontally to the far end of your cooking chamber.
Check the opening between your firebox and cooking chamber. Look to see where it is located in reference to the grate....is it above the grate or half way above or below. Here again, your hot air will come blasting out of that opening and go directly thru your meat over to the now extended exhaust. That means it will be very hot at that opening. A simple solution is to put a large pan of water right at that opening. This will deflect much of the heat and will tone down that hot spot.
A surer fix is to attach a "baffle plate" to the top of the opening and bend it downwards so it deflects the heat UNDERNEATH the grate. No welding required but you would have to drill a couple of holes and simply use nuts and bolts to attach. The thicker the metal the better the baffle.
The firebox also leaves a lot to be desired. I have seen charcoal baskets that help to keep the charcoal all in one place and allow for some air circulation. Folks using these claim much longer burn times and much easier temp controls. Why?? Once your charcoal starts to burn down, the live coals get smothered and choked out by the ash. By allowing air flow, your temps will stay where you need them and are much easier to control because of the added air.
Here is a link to charcoal baskets and also pics and further explanation of the mods for some specific cookers........... http://www.teddybearbbq.com/getstarted.htm
Once at this site, at the top of the page are 2 links....Smoker Mods and Charcoal. That is where you will find the info.