l7809cv voltage regulator: heat sink or not?
As a ballpark figure a TO220 component can dissipate 1 Watt without a heatsink (but proivided that the air can flow around it). 9V * 100 mA = 0.9W, so you are near the edge but still within the limit.

When dissipating 1W the component will definitely get too hot to touch. If that is a problem (for other components, or for humans) you will have to provide some heatsink. Even a very small heatsink, let's say rated at 20C/W, will reduce the temperature considerably.