Years ago, when I bought some sourdough cultures from Sourdough International, I built their suggested fermenter: a styrofoam cooler fitted with a light on a dimmer switch. I use a 25 watt incandescent bulb. Make the light brighter for warmer, dimmer for less warm. I poked a food thermometer through the side of the cooler to gauge the temp inside. I have used the same contraption for proofing bread and culturing yogurt for 10 years, and haven’t replaced the bulb yet
Thickness usually does come from heating the milk enough to denature some of the protein. I wonder if you could supplement your milk with powdered milk or liquid cream to get it thicker. You might also try food grade calcium chloride, which is used in cheese making.
Good luck with your endeavors!
Scott