I'm using the low-cost non-adjustable heater from Wal-Mart, and it keeps my water at about 77F constantly. My room temp varies from 60 F to 75 F. One night I think it got as cold as 55. Mine hasn't had any problems.
I think the wattage will make a big difference as to if it can keep a consistent temp. It seems to me that an in-tank heater with sufficient wattage would keep the water temperature near where the thermostat is set.* I couldn't image how room temp would affect a submersed thermostat. So as long as your not trying to heat a large tank with a 10 watt heater, you shouldn't have any problems.**
* The biggest problem I've read with preset heaters is that the thermostat isn't always accurate, but they should hold a steady temp even if that temp isn't exactly what is advertised.
** I've read that you shouldn't use too large a heater in a smaller tank either because you could over-heat the water and cook the fish. Again, that's what the thermostat is for. The water will heat faster with a higher wattage, but the thermostat should still cut the heat off at the correct temperature. But then again I haven't tested this aside from sticking my 50 Watt in a one-gallon vase while cleaning my 3 gallon tank. This one heater has been in one, three, and ten gallon tanks, and has maintained the same 76 - 77 F temp.