Air cooling will never get you below Ambient temps.
Water cooling will get you to ambient or a bit under
Dice will get you to -100C or thereabouts, but will degrade if you don't keep adding it
And LN2 will get you to roughly -200C
To my knowledge Phase gets you somewhere in between DICE and LN2. LN2 and Dice cannot be used for 24/7 cooling. Only for benching, but they are much cheaper than phase and WC.
when it comes down to it, everything that uses a closed loop is air cooled (that is to say everything but LN2 and DI)
Water cooling can never achieve below ambient temperature either (unless its rapidly evaporating... which = BAD) without a chiller, because the water is simply being cooled by a large air cooler which wouldn't fit in your case...
CO2 sublimes (changes from solid to gas, or vice versa) at -78.5°C... when it sumblimes, like any change of state, it involves an energy transfer... for our purposes, this is an absorption... as such, the subliming DI keeps the surface it is in contact with (usually acetone or ethanol/methanol because they won't freeze until below -90°C) at that sublimation temperature (until it has all become gas, of course)... but because there is a pot between the die and the coolant, a heat transfer must occur here... the transfer continues until an equilibrium is reached... because one side of the pot is hot (the die) and the other is cold (the DI suspended in low temp fluid), a temperature between the two must be achieved such that the energy released = the energy absorbed (this is optimal, under normal conditions, the equilibrium is far harder to achieve and thus the temps can be affected)... as such, the interior temp of the pot might be around -70°C, but the actual die temp could be around -40°C
Nitrogen boils vapourises at -195.6°C... a mechanism similar to that of DI is employed here, except there is no need for fluid (as the nitrogen is already liquefied)... the equilibrium temp will obviously be much lower here, but being as the spread is much higher, the main factor influencing the final temps achieved is the design of the pot... the ideal pot will be able to reach a foot temp of approximately -190°C, but this is practically impossible... instead, a common pot will have temps around -150 to -180°C, which translates to core temps of about -130 to -110°C purely because the latent heat of vapourisation of nitrogen is very low (3rd lowest of any element @ 2.79kJ/mol... hydrogen and helium are lower)
the temperatures achieved by a phase change system depends on its design... that is, whether it is a single stage or cascading multi stage unit, the design of the evaporator and quality of the build also have a noteworthy effect on the achieveable temps... phase change systems use a compressor to increase the pressure of a gas refrigerant such that the boiling point increases... this is done until the boiling point is at ambient temperature, at which point the gas condenses to liquid... the gas is then decompressed through a capillary tube which brings its boiling point back to normal, allowing it to absorb heat from a CPU by being boiled in an evaporator (a substance absorbs heat when changing from liquid to gas... you can try it... biol a pot of water and watch the temp... itr'll never pass 100°C... this is known as latent heat)
single stage units will usually reach nozzle temps of around -25°C using R134a (cheap ,low quality refrigerant... usually used by first time builders) or about -45 to-50°C using R143a/R507 (industry standards, very common in performance single stagers)
cascades are able to achieve much lower temperatures, as they use the primary refrigerant to cool a heat exchanger, which allows a secondary refrigerant to be condensed using lower pressures (this can be repeated as many times as necessary)... 2 stage cascades will generally be built using R1150 (ethylene) and can achieve a nozzle temp lower than -103.1°C, although because adiabatic systems are very hard to design and build without alot of training and experience, the temps are generally higher, but still around -100°C... a three stage unit will usually use R14 (tetrafluoromethane), which allows nozzle temps around -128.8°C. the largest cascade on record is a 4 stager by cold_ice... this uses methane as a quaternary refrigerant... methane can achieve temps as low as -161.6°C, but under load the temps are usually higher, because methane's ability to hold a load is extremely poor (ie its latent heat of vapourisation is quite low... 8.17kJ/mol...water is 40.68kJ/mol)