The apc1000 and similar rack mount pure sine wave machines have heatsinks and fans and if you could easily add a heatsink and fan on the side of the transformer.
you can find them on ebay and sometimes craigslist for pretty cheap. here's one.
http://www.ebay.com/itm/APC-SU1400RMXLB3U-SMART-UPS-1400-1400VA-120V-UNINTERRUPTIBLE-POWER-SUPPLY-TESTED-/231395330666also, many pure sine wave back up supplies such as the one above do not have an external inductor but rather use the leakage inductance of the transformer for two purposes:
1) as a boost inductor for charging the battery.
2) as a filter for producing the sine wave output.
Installing a suitable inductor in series with the low voltage side of the transformer is worth the effort. you'll get a reduction in parasitic draw from the outlet of about 5-10 watts and the efficiency will increase during inverting operation significantly.
in that ebay link, the batteries (not included in the auction) connect through a 50 or 75 amp anderson power pole connector and they might be 10 awg wires.
if you have scrap copper lying around i would make them 8 awg minimum.
also the 1 foot leads between the transformer and the H bridge are 10 awg when they should be 8 awg wire. you can replace them too.. that's 1 more milli ohm removed from the system.
adding a second capacitor to the H bridge board is also possible because the ESR of the capacitor itself will suck up about a watt.
that particular unit probably has 16 mosfets.. you may get lucky and be able to add 4 more (some have room for 20)
if there are only 8 or 12 fets, you will almost certainly be able to add 4 or 8 more, this is certainly worth the effort.
i recommend buying the same fets, not mixing different part numbers.
Even if all you do is heatsink the transformer, you should still be able to get continuous duty operation from this series of inverters.
if you buy brand new AGM cells you shouldn't have any problem up to about 10 times the design amp hours of the system.
I would buy flooded cells and check the water level every 3 months... they will last a lot longer than the three+ years you'll get from agm cells.
the only danger of an infinite battery supply is the self discharge rate exceeding the charging current.
i don't recall if these inverters push the battery volts all the way up to 14.5 volts and then float it at 13.8.
but if the battery is flooded and very large, or if its agm and extreemely large, the inverter won't be able to provide enough amps to push the terminal volts all the way up to 14.6 volts or whatever it is.
thus it will eternally dump 1 or 2 amps into the battery and you'll be boiling the water out of the batteries and they won't last long if they are agm cells.. or you'll be adding water rather often to flooded cells.
an external charger will solve this problem but it creates a few more..
(even the 13.8 volts is too high a float voltage but there is little that can be done with APC equipment to reduce this voltage ... they enjoy selling replacement batteries too much)