I don't recommend this at all.
Working heroic hours (working at home is the same as staying late in the office) may seem like a good idea, but it almost never is. Your employer will come to rely on and expect your extra productivity "that's just Andrew, he doesn't have a life, he works late etc." You probably won't be rewarded (either with a raise or with excessive recognition), which is something you might come to resent if it goes on long enough. I've definitely got myself sucked into this and gotten a martyr complex over it, so I'm calling myself out here.
Instead, think about going through proper channels at work. If a casual suggestion seems to interest your manager, write up a proposal and ask to present your idea. Argue logically about why you think something needs to be done better and how it will "help the company" (yes I know, Office Space reference) -- save money, raise revenue, reduce risk etc. If it's actually a good idea, then they will be happy to allocate staff time (which == money) to it, but if it's not worth anything to them, then it's not worth you doing it for them for free.
Worst case, you'll get some credit for being inventive and showing initiative. Managers love it when you show you can communicate effectively with non-techie "business" managers.
If you are doing extra work that isn't called for, be very clear up-front about it. Your company may actually want you not to work extra on things they don't necessarily care about and wear yourself out. Most studies show that people only have about 5 hours of really intensive mental focus productive time to give each day -- you don't necessarily want that time to go into your "fun" projects and have the things that matter to your company suffer, either.
Even if your bosses do like the idea, be sure to set boundaries -- tell them that you are just developing X or Y component to scratch an itch and you hope you will be rewarded in some way at work if it pays off for the company. (And be sure to follow up and ask for a raise if it does! Even if you don't get a raise right then, they will remember better.)
We all have ideas for fun projects, and often these are naturally suggested by things at work, because we spend a lot of our time working and thinking about work. But, if your company doesn't go for it and you really want to scratch the itch, try to think of a way to spin it off as a separate project you can do on your own. This is how I've wound up contributing to FOSS projects (geez, framework X really needs a Y!) which brings psychic rewards, and it's also how lots of companies like Intel and Google got started. :)