Sorry for the delay in the answer. From what you are describing and since it's temp related it sounds like the issue is with the ecm relay in the IPDM. This is the large fuse and relay box under the hood. Losing both spark and fuel injector pulse if it were due to a cam or crank sensor should leave a stored code in the computer. Since you are losing both, and don't have any codes, it indicates to me an electrical failure for the computers power.
This could be a bad connection on the IPDM, the ECM relay in the IPDM or the wiring at the ecm.
On the 2011 the ecm relay isn't replaceable without replacing the entire IPDM, in fact the service manual doesn't even show which relay is for the ecm. The older models did, and we could do a swap to determine if the relay were the issue or not.
In this case what I would do is this, when it's cold and you don't have any spark or fuel, take a blow dryer and heat up the IPDM. Then see if you get it to start, if you do, then replace the IPDM. If not, then you may have to take it in and leave it over night for scan tool diagnostics when it's cold. With a good scan tool, we can see if one of the other sensors is causing the issue.
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Thank you so much!