Now CO² in gas form is extremely temperatur sensitive, the presure rises when temp rises. So with a regulator containing only 1 membrane (Single Stage).
These slight changes also result in a somewhat fluctuating output. But pressurized liquid CO² is rather darn cold and keeps all gas form above it cool enough so this is rather unnoticable. When the bottle is near empty there will be no more fluid CO² in the bottle and there is no more cooling property. It takes on the invironmental temperature from the room the bottle is in and the CO² expands exponentialy for a brief moment resulting in a drastic increasing pressure possibly above 50 bar. The famous tank dump. The single stage membrane spring cannot hold this sudden increasing presure to it's set value and this also increases the output.
Nothing to do with cooling at all. The CO2 is liquid at room temperature AND a pressure of 55bar. As an aside liquid CO2 does not exist at normal atmospheric pressure, only gas and solid.
A single stage regulator "with a membrane", as you say, will keep fine regulation provided the tank still contains liquid CO2 at 55bar pressure. No problems there. What does happen when the liquid runs out and only gas is left the tank pressure starts to drop and the output pressure also drops. My single stage regulator starts loosing its 2.6bar output pressure when tank pressure drops below 30bar odd. Generally in quality single stage regulators as the tank empties the output pressure just drops, no dumping, just your CO2 injection rate drops as output pressure drops. With my 2Kg fire extinguisher and single stage regulator this takes 3-4 days after tank pressure starts dropping before CO2 injection bubble rate drops. Normally enough time for me to notice and change the tank. If I leave mine CO2 injection rate just slowly drops to zero as tank empties. No issue.
With a dual stage regulator on regulator reduces the pressure to say 14bar and a second stage, usually adjustable as well, reduces this 14bar to say 3bar. Because of the dual stages the output pressure does not vary (too much) when the tank starts to empty, the output pressure stays constant until the tank pressure reaches 14bar, where it then all stops. Some people like this as it gives another CO2 knob to fiddle (output pressure) and you won't have algae & plant problems due to carrying CO2 levels as tank empties. However the downside is, you will get no in tank notification CO2 is running out ie reduced bubble rate, as the CO2 will just stop when tank is empty. This is a problem/difficulty if you locate you CO2 in a cupboard where you cannot easily observe the tank pressure gauge easily/daily.
However there are a third class of cheaper regulators that are not really regulators but flow control valves that produce reduced pressure ie 3bar from 55bar tank pressure by using a pin hole or metal sponge to restrict gas flow. These work fine, but suffer from the issue of complete loss of regulation when tank pressure starts to fall and can vent the remaining tank contents. This is brilliant if you are CO2 welding, you get a rush of gas, disrupting your weld which tells you to change CO2 cylinder. In a fish tanks this emptying of gas is probably fine if you are using a 14gr or 95gr disposable canister, the end of tank dump is not much gas, no problem. However if you are using a 2Kg cylinder the end of tank dump can be a considerable quantity of gas, this asphyxiating all your fish.
So dual stage is nice, if you can afford it, but single stage is also ok.
