Smoking cheese is typically done as cold-smoking (no heat). The cold-smoking method, smokes the cheese between 60° to 86° F. Any cheese may be smoked if the temperature is kept cool enough. The primary reason for keeping cheese cool is that the melting point of the butterfat, which is 98°. The butterfat will actually begin to ooze from the cheese when it reaches temperatures in the middle 60’s; this is often referred to as “sweating”. Since we do not want to strip the butterfat from the cheese during the smoking process, we need to keep the smoking process as cold as possible.
When sorting through the different methods of cold smoking, the main fact you have to understand is that you are cold smoking so that the cheese will not “sweat” or melt from heat. It’s not really a difficult process, but if you over think the technique you can make things more complex than they need to be.
Cold smoking usually refers to smoking foods at temperatures of about 90 degrees or less, something that might be difficult with some backyard smokers. Most books state that cheese should be smoked under 80 degrees, but you will probably want to smoke your cheese below 60 degrees, if possible, so the cheese will not “sweat”.
Smoking above 90 degrees will cause some cheeses to melt; the last thing you want is to end up with a melted cheese mess in the smoker.
Personally I like to keep things about 50-55 degrees when working with cheese. You can add trays / pans of ice into the cooker to keep the temperatures down during smoking. You can also take advantage of cooler outside temperatures to help achieve the lower temperatures associated with cold smoking.
I do a lot of cold smoking in the fall, winter, and early spring when conditions are near perfect for cold smoking cheese and other foods. I like to cold smoke using the A-Maze-N Pellet Smoker, it's simple, easy, and produces virtually no heat.
Here's a link to a tutorial I posted a while ago if you are interested.
https://www.bbq-brethren.com/forum/showpost.php?p=4388620&postcount=7