Old topic, but there aren't any others containing data for the Acurite 606TX. I tried one yesterday but it went bad within a few hours. In that time, I was able to record some data from RTL_433. It's a different format so I don't know for sure that it's valid, but I figured it might help someone. Note that the first 3 readings were recorded after the battery was removed and reinstalled. From what I've read, the unit ID may roll automatically every time the battery is removed/installed so the ID bit(s) may not match.
degC degF
[01] {32} b6 8f 55 44 00 : 10110110 10001111 01010101 01000100 00000000 -17.22222222 1
[01] {32} b6 8f 73 c2 00 : 10110110 10001111 01110011 11000010 00000000 -13.88888889 7
[01] {32} b6 8f b4 c6 00 : 10110110 10001111 10110100 11000110 00000000 -7.777777778 18
[01] {32} b6 80 cc 7b 00 : 10110110 10000000 11001100 01111011 00000000 15 59
[01] {32} b6 80 c9 0c 00 : 10110110 10000000 11001001 00001100 00000000 20 68
[01] {32} b6 80 d0 a1 00 : 10110110 10000000 11010000 10100001 00000000 20.55555556 69
[01] {32} b6 80 d5 d6 00 : 10110110 10000000 11010101 11010110 00000000 21.11111111 70
[01] {32} b6 80 db bb 00 : 10110110 10000000 11011011 10111011 00000000 21.66666667 71
[01] {32} b6 8f e7 0c 00 : 10110110 10001111 11100111 00001100 00000000 21.66666667 71
[01] {32} b6 80 e6 49 00 : 10110110 10000000 11100110 01001001 00000000 22.77777778 73
[01] {32} b6 80 ea fd 00 : 10110110 10000000 11101010 11111101 00000000 23.33333333 74
[01] {32} b6 81 07 8d 00 : 10110110 10000001 00000111 10001101 00000000 26.11111111 79
If this turns out to be of no use, no problem. Enjoy!