Sundance--I'm sorry if I offended you, it certainly wasn't my intention.
Alan--it depends, I suppose. I would expect most tanks big enough to happily house an adult bimac would have enough temperature "inertia" to minimize that daily variation. What kind of variation are we talking about? If we're just talking 5 degrees or so, maybe 10 tops, I think you'd be much better without the heater. And I can't imagine, even in chilly Pennsylvania, that you have more than a 10 degree variation.
Here's my uninvited diatribe:
What's "proven to work" is very subjective at best in this hobby. You can find a 100 people who collectively "prove" that a tang and a puffer can be kept in a 29 gallon tank. Likewise there's someone who posts occasionally on TONMO about how great his bimac is doing in an Eclipse--Nevermind the fact that it is completely infested with hair and bubble algae, he proved its possible! This is especially true with the octopus hobby which is truly still in infancy. There are so many things about them that have been repeated on this and other forums that are--simply and demonstrably--false. Things like the size difference between O. bimaculoides and O. bimaculatus.
Given this, when planning my systems I try to focus on two sources of information: the environment the animals come from, and the peer-reviewed scientific literature. In the case of bimac temperatures, the annual variation in water temperature varies from about 57 degrees in January to a summer high of 69 degrees at Oceanside, CA. The low 70s are a realistic compromise to keep bimacs in a home aquarium without a chiller, but nonetheless one that will shorten their life. Keeping a bimac tank in the upper 70s is like keeping your reef in the mid 90s! Given that many bimacs are naturally intertidal, considerable daily fluctuations are almost certainly more natural than a 24-hour slow roast.
The peer-reviewed literature is also most helpful because bimacs have been raised and brooded by the tens of thousands at the NRCC is Galveston, and every excruciating detail about what works and what doesn't has been published--20 years ago, no less. To paraphrase my favorite marine biologist (George Lewis Costanza), while us hobbyists have been rubbing two sticks together, the biologists are out there walking around with Zippos.
I don't mean to come off as a jerk, but I stongly feel that if we're to keep these or any creatures we should know a little more about them than just what the LFS tells us about it to sell it to us (which is unfortunately less research than most octo owners even do! How many messages are posted on TONMO that say "help I just bought an octo what do I feed it?").
Dan