I did a temperature project maybe 1 year ago and the environment was very cold then I used Lithium Thionyl Chloride batteries. In that project I used LS 14250 from the company saft.
It's a 3.6V battery with the size of 1/2 AA and a capacity 1.2Ah and with a operating temperature range -60°C to +85°C.
In the system documentation for the mcModule 110 then the input voltage recommendation is +2.1V to +3.6V (+3.0V Typical) So I think this battery would be great for this task.
So maybe a enclosure that's include space for a 1/2 AA and the module would be good here.
And in the freezer i don't see a problem with the "extra" size of the module, do you?