Mine is outside, its a non named ebay purchase for £25 so its doing quite well and yes it is wireless, transmits through the double glazing no issues. The batteries have to be replaced regularly when the weather is sustained at around 1c or lower like recently. So I have been using Lithium Ion rechargeables which last longer.
-4.9c now. Left Horfield at -2c, rose to 0c by the M32, back to -4.9c when I got home.