To measure current, just use a current sense IC . . .
For temp measurements, my multimeter has a built in thermometer.
If I were to use an temperature measuring IC like you mentioned, I would actually use two. One would measure ambient/noise (not connected to anything), and one would measure ambient + something_else (connected to something).
Then just subtract the readings to just get something_else without the ambient noise (a breeze, light differences, etc).