You would think that $4 would pay for some excellent refrigeration equipment. I wonder what the engineering compromises are for the LNG storage on these ships.
LNG is almost all methane which is the lightest hydrocarbon. Methane is so light a gas that it does not liquefy even under thousands of PSI of compression. And at room temperature it only practically exists in a gas form, pressurized or not, so in that case it needs to be handled like oxygen or nitrogen, other light gases where the heavy-walled steel storage cylinders weigh more than the contents even at maximum pressure.
You just can't get that many kilos of such light molecules into a certain space as a compressed gas compared to how dense a liquid gets.
So they liquefy the gas instead before transport and that requires cryogenics rather than pressure. The chilled liquid can then be stored or transported in tanks of much thinner-walled steel since gas pressure is not a major issue. These low-pressure tanks are thickly insulated with lightweight materials to keep in the cold as much as possible.
And unlike the heavy-walled things like the welders use for their pressurized oxygen, cryogenics are handled like the tanks of liquid oxygen, where you can't completely close the cryogenic storage tanks or pressure would build up beyond the bursting point of their relatively thin-walled construction. The cryogenic tanks are constantly hissing as they release excess gas for this reason.
Since no insulation is perfect, the cargo does pick up heat gradually and this causes a certain amount of steady boiloff. Rather than physically becoming warmer, the cargo self-refrigerates by evaporation.
Basically they are loading metric shiploads of really cold LNG and it just slowly evaporates as they go. The cargo temperature is kept constant by self-refrigeration where the condenser is the plant on shore and the evaporator is the ship on its way at sea.