Biomolecular networks can dynamically encode information, generating time-varying patterns of activity in response to an input. Here we find that dynamic encoding can also be performed by individual proteins. BcLOV4 is an optogenetic protein that uniquely displays pulsatory activation in response to a step input of light, and response dynamics can be shaped by both light and temperature. However, how the BcLOV4 protein generates this step-to-pulse response is not understood. Here we combined live cell imaging and simulations to find that the activity pulse results from an intramolecular incoherent feedforward loop (IFFL) implemented by competitive interactions between protein domains that separately respond to light or temperature. We identified these light- and temperature-sensitive regions and found that they implement the IFFL by competitively caging an activation region. Structural and sequence analysis revealed temperature-responsive regions of BcLOV4 which allowed experimental tuning of activation dynamics and suggested that tuning has also occurred throughout evolution. These findings enabled the generation of more thermostable optogenetic tools and identified a modular thermosensitive domain that endowed thermogenetic control over unrelated proteins. Our findings uncover principles of dynamic and combinatorial signal processing in individual proteins that will fuel development of more sophisticated and compact synthetic systems.