With making koji and tempeh, having a muro or incubation chamber is a huge help. You get more consistent product and the process becomes more predictable. Most microorganisms have preferred environmental conditions. The closer that you stay to these conditions, the less other microbes you will grow that will ruin your batch. Too hot, too cold, too dry, and too saturated with moisture are all potential problems when making koji and tempeh.
Since I mostly write this for those who are making batches for home use, a good place to start is a wooden box. The wood gives some insulation and deals well with the moisture. With the high humidity, you don't end up with the condensation that you would with uninsulated metal walls. In addition, it can be used as home decor, instead of looking like a large alien object. I have built and advised on some for whom square footage or floor space was limited, so I built tall muros that would hold 6 koji trays at a time. My muro is four feet wide, three feet deep, and three feet tall. With this arrangement, I could fit about 20 trays, but haven't used near that many.
The temperature and moisture can be set using a few controls with a heater and a humidifier. For the temperature control, you can order an STC-1000 or a PID controller such as those from Auber Instruments. Both are affordable, especially if you have the minimal tools required and the wiring. You will be able to keep a narrow range of temperature this way. For the humidity control, you can get a WH8040. There are hundreds of wiring diagrams to be found online for how to wire these up so I will leave that to you. An overview of the typical setup: put both humidity and temperature controls in a project box with each wired to separate electrical outlets. The nice thing about this is that you can use this control combination for many purposes, including egg incubation, starting seeds indoors, meat curing chambers and more. You could even switch out the heater with an air conditioner, or the humidifier with a dehumidifier, for achieving other optimal climates. I do sell muros, which include the wiring and the box, typically affordable items in addition to my labor.
For a simpler and more expensive option, there is also a "plug and play" from Auber Instuments Model TH210 that I haven't used but looks promising. There is no wiring to do with this product - you just plug in the heater and humidifier that you purchase separately, and then set the temp and humidity level on the control box.
For home use, my preferred heat source is a ceramic space heater, which moves the muro back up to temp within minutes, keeping your koji happy. They maintain the heat well also, while having lower fire risk compared to many other types of space heater. All in all, they make for the best of the heat options, combining ease, safety, and quality. Don't buy the smallest and cheapest heat source that you can get. Some will have faulty heat controls.
For humidity control, the best humidifier to get is an ultrasonic humidifier. You will have the least microbial issues. You don't want a warm mist type, cool mist type, or any with a filter. Also, always remember to dump your humidifier out after use to allow it to dry if you won't be using it for awhile to prevent unwanted mold.
In Japan, both in home scale and industrial scale, koji trays have been a major component of koji incubation. The trays are an added insulator that also wick away any excess moisture that could pool in other more non-porous containers such as glass or metal. The koji substrate needs oxygen and airspace and excess water can cause undesired bacterial growth. During the process of making koji, the chemical process begins to create heat called "self heat." The koji can overheat causing bacterial growth as well. The optimal koji environment must be maintained for it to finish out properly. It must not overheat, nor do you want to gravely drop the temp. The trays help maintain some heat from which is being created by the koji itself, even while the heater is off. By shaping the growing koji in furrows, you prevent hot pockets and allow for some of the heat to escape.
If you want to build your own muro, I hope you find this helpful. Feel free to contact me with questions. Hit me up either way if you make one with this format; it would be fun to know people are finding it useful. For those wishing to have one made, contact me and we can come up with something to work for your needs and home.