Yes, THERMOGRAPH is a Scrabble word!

Letter values in Scrabble US: T 1, H 4, E 1, R 1, M 3, O 1, G 2, R 1, A 1, P 3, H 4.

Is it a valid word?

THERMOGRAPH is a valid word in the official Scrabble dictionary (US), the UK Scrabble Dictionary and Words with Friends (ENABLE).

medical instrument that uses an infrared camera to reveal temperature variations on the surface of the body
a thermometer that records temperature variations on a graph as a function of time

Also: thermometrograph.