How much temperature control does an emergency food cache need?
Short answer: you need to keep those goods above freezing, below 85F, and in a low-humidity environment.

Long Answer: 

Freezing: Canned goods, jars, and tetrapaks that are frozen can leak, split, or even explode, and are often unsafe to eat after thawing.

Heat: canned goods safe and nutritious lifetime decreases at temperatures above 85F, and US regulations allow them to fail preservation outright at 100F (which means some).  TetraPak also recommends against exposing those milk cartons to temperatures above 100F for more than 24 hours.

Moisture: cans and jar lids can and do rust, and if the rust penetrates into the interior can cause seal failure.  While TetraPak provides no information about failure modes, they also recommend storing cartons in a dry environment.

So, if you want those supplies to be wholesome and nutritious until their printed expiration dates, store them between 33F and 85F in a dry place.  In Florida, that might be a challenge, but in the NW USA, you can solve that by putting them in a well-lined, well-drained cellar.