HC-SR501 PIR MOTION DETECTOR low temp failure

Other Hardware Sensors
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I am using multiple HC-SR501 PIR MOTION DETECTORs to detect animals outside chicken coops: specifically coytoes, wolves, etc. Above ~ -12 degrees F they all seem to work fine. I bought them from China on eBay. One data sheet said they are good to -15 degrees F, another data sheet says good to -20 degrees F.

last night was -12 F and they all failed to detect the coyote that prowls around (confirmed the animals were there with my trail cam and the foot prints in the snow.

Does anyone know of PIRs that can work below -12 degrees F ? My trail cams operate with no problem below -30 so such a thing clearly exists.

Thank you all!

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PS: I have checked and the problem is not low battery: the batteries are new and fully charged and volt meter says full charge. Its not a power issue: when i warm the PIRs they seem to come alive. When the cool too low they fail to detect.