If you depressurize an aircraft at FL340, will the temperature inside fall to match the temperature outside?
This depends entirely on how you depressurized it. 

Depressurizing the aircraft by fully opening the outflow valve will lower the temperature somewhat, but will not bring it to that outside. 

The expansion process will be closest to free (Joule) expansion, which causes only small decrease in temperature, not an adiabatic one that corresponds to the atmospheric lapse rate. And while some energy will be lost through the air's initial expansion as it escapes, it will quickly be replaced by new warm air coming in through the packs (cabin pressurization and air conditioning system).

That air supply is quite reliable, as it's bled from engines at about $200\ \mathrm{^\circ C}$ – it then needs to be air-conditioned so as not to roast the passengers. The packs will automatically maintain set temperature, putting less effort into cooling the air if the cabin gets too cold. 

If you also disable the engines, so no new air can come in, the airplane will lose some heat. Still, in all other regards, the fuselage will remain a well-insulated vessel with some heat sources on the inside. Also, the less-dense air is much less effective at heat transfer, and has much less heat capacity, so it will get chilly, but the passengers aren't going to freeze to death or even get a frostbite.

The heat capacity of air at ambient pressure will be about $280\ \frac{\mathrm{J}}{\mathrm{m}^3\cdot\mathrm{K}}$. A 737 encloses about $200\ \mathrm{m}^3$, giving a total of $56\ \frac{\mathrm{kJ}}{\mathrm{K}}$. For comparison, the plane's passengers have a specific heat capacity of $3.5\ \frac{\mathrm{kJ}}{\mathrm{kg}\cdot\mathrm{K}}$, giving, for 120–160 of them, about $40\ \frac{\mathrm{MJ}}{\mathrm{K}}$. So a $\sim70\ \mathrm{^\circ C}$ one-time drop in air temperature can technically match the outside, but it can only cool the passengers by at most $0.1\ \mathrm{^\circ C}$. 

In practice, the cooling won't be instant, and it has to compete with heat exchange with the still-warm interior. Passenger bodies producing $12{-}18\ \mathrm{kW}$ of waste heat (at rest) will also restore cabin air temperature by $\sim1\ \mathrm{^\circ C}$ every 4 seconds. The larger the hole, the lower the temperature minimum that will be reached. With a broken window, the effect of this one-time expansion heat loss will have been mostly undone before anyone notices it, amidst the chaos.

Tearing the top of the fuselage off, on the other hand, will most definitely let the passengers feel the cold outside. But it will be the powerful wind blowing in, not the air leaving the airplane, that will chill its interior. 

Breaking a single window or making a lot of bullet holes (really a lot - it will take a crate of ammo to overcome the packs' air inflow) is about the same as fully opening the outflow valve. It will produce some cooling effect, but it will definitely not bring the interior to the outside temperature, as the cooling effect is one-time, and will be rapidly compensated for.

This kind of event has happened a few times in aviation history. It has caused some fatalities – a person sitting right next to the broken window has been killed by the mechanical force of the escaping air. No one has been frozen to death, not even in the Aloha Flight 243, which represents about the worst possible case for depressurization (which still leaves survivors and not just a debris field).