FLW houses are notoriously hard to heat - he was intransigent about insulation, double-glazing, etc and insisted he knew best (read, for instance, "The Natural House" where he says stuff like that*). While radiant heat is great when engineered correctly, he often didn't engineer it properly and didn't allow contractors to adjust the design to heat better. When the builders insisted it would get done right. His first solar houses were awful too - the Kecks did it way better (Keck & Keck, Chicago area modernists & solar pioneers, almost as prolific as FLW but not as well known - they did almost exclusively large suburban & rural houses).
He would do AC when forced to or the budget allowed - I believe (but not 100% certain) that Wingspread - the Johnson residence north of Racine - had it from day one. It's bigger problem was the leaky skylights. This one is open to the public and if you visit, you'll get the story of Hib Johnson calling up Ole' Frankie at Taleisin West during a dinner party in the presence of the Governor of Wisconsin and one of the state senators to complain about the leak... It's a free tour (with reservations required) and you can do with with the SC Johnson HQ that he designed - you get to see the research tower now too.
One wonders what he would have made of "open plan" or open concept - he always (or usually/often) tucked the kitchens away as "workspaces" in a rather misogynist manner. And they were often too small to boot.
I've been in several of his houses (most recently a very large and expensive one in the North Shore of Chicago) and they can be incredible - genius even - but difficult to live with because of that. This one looks so impeccably maintained that keeping it that way should be easy.
* He had the right idea at the Robie House, but it wasn't fully installed or designed - Reynor Banham talks about this in his book "The Well-Tempered Environment" however, others argue that he is incorrect. There was a well or pocket under the south facing windows (which are shielded perfectly from summer sun) which had a steam pipe installed but not "radiator" or convector which would have washed the windows with heat (the north windows, not to the floor, have radiators concealed under them) and the house required big, honking free-standing radiators to be installed to heat the main rooms.
