Mushrooms need 13-14 degrees C with 90% humidity. This is a higher temperature than a root cellar naturally maintains and at the same time a higher humidity than cold rooms naturally support. Two low tech ways you can obtain the temperature in a root cellar is with an insulated root cellar “cold frame” and by taking advantage of the heat producing properties of composting manure. There is a free book on the internet that describes many low tech solutions for growing mushrooms.
The book is “A Practical Treatise on Mushroom Culture for Profit and Pleasure” by William Falconer, 1901. digitized by Google at the Harvard Library. This book is free online as a PDF download and here is the link: