This work presents the fabrication of crumpled carbon nanotubes (C-CNTs) thin film heaters and their application towards high sensitivity and low drift hydrogen gas sensing. Utilizing a spray coating of pristine multi-walled carbon nanotubes (MWCNTs) and thermal shrinkage of polystyrene (PS) substrate, we have fabricated C-CNTs with closely packed junctions. Joule heating of C-CNTs gives higher temperature at a given input voltage compared to as-deposited CNTs. In addition, temperature coefficient of resistance (TCR) is analyzed for accurate temperature control and measurement of the heater. The C-CNT heaters are capable of hydrogen gas sensing while demonstrating higher measurement sensitivities along with lower drift compared to as-deposited CNT devices. In addition, the self-heating of C-CNT heaters help rapid desorption of hydrogen, and thus allowing repetitive and stable sensor operation. Our findings reveal that both CNT morphologies and heating temperatures affect the hydrogen sensing performances.