Can 'Shrooms be grown in my grow closet, too?

My DH has decided to grow shrooms. He wants part of my grow closet to do so. I am all good with that. I am just worried about the higher temps needed to grow mushrooms. Will the higher heat hurt my plants? At present I have only one seedling and 2 new seeds germinating. I killed my first batch because I was worried about the closet getting too cold at night( it's in my basement) and put on the space heater I have way too high. Temps soared to over 100 during the dark period. So, now I have an average low of 70 and high of 77, depending on how cool it is out. My new seedling is looking great! I don't want to make the same mistake twice, bad enough it happened once!
Any input would be appriciated! I also posted this question on the Hallucinatory (spelling, sorry).
I wasn't sure where I should post this, so I picked both!

ya man u can def. grow shrooms in ur growroom they like the climate just make sure they dont get light and ull be all good especially if ur temps at 70s to 80s. how are u planing to do em? u can use perilite if u have any left over from a grow and if there a small strain u can just cover a coco cup. its pretty simple

I found a post that gives step-by-step info. on the hallucinatory substances. I am planning to follow those instructions! I'll or DH wiil use the brown rice, vermiculite and water for the cakes. They will go in half pint canning jars and be sterilized in my pressure cooker. After incubation, into translucent rubbbermaid container, the type that fits under a bed. The bottom of the container will be lined with damp perlite to humidity high. Really, I am sure I'll be helping a lot, but it's DH's show! I am just his research assistant!
Thanks for the help! Rep+!