My understanding is that in the case of heat death, if this state continues to persist for infinite time, then every possible event that can happen will eventually happen due to sheer infinite time and every possible thermal fluctuation that can happen eventually happening; although of course much smaller fluctuations are always more likely than bigger ones.
A brain fluctuating into existence and then existing for long enough to take an instantaneous mental action is absurdly more unlikely than the brain popping into existence and then scattering just as fast; but the infinity, if true, would make infinite such brains inevitable and much more likely than real brains.
Again, this is just my understanding of the argument as an amateur, definitely not a professional in this and I think there are physics and epistemics arguments which might overcome this.
Haha not often, but they read blog posts written by other Boltzmann brains even less often.