Ebedded Linux: Recoverable, battery backed-up RAM (/tmp)
Keeping power is not enough to preserve regular SDRAM contents. At the very least, you will have to provide clock and periodically send the "refresh command" if you need to preserve the contents for more than a few milliseconds or tens of milliseconds. If your system allows to keep the DRAM controller working while the rest of the system is off, try doing that when you power off.

If you can source PSDRAM (pseudo-static DRAM) or self-refreshing SDRAM (example), you won't have to worry about refresh, as the SDRAM controller will be embedded in the RAM itself. This is what some mobile phones and other portable gadgets use to reduce current consumption in sleep mode. You'll still have to provide clock for it to work.

Note that tmpfs is not designed with any kind of persistence in mind: the filesystem simply gets recreated from scratch every time you mount it. Also, /tmp is the wrong place to keep persistent files anyway. Even if you get to preserve RAM contents and write a persistence-aware filesystem driver, Linux is free to wipe the /tmp folder when it reboots.