Would either of these BJTs require a heat sink?
Heatsinks are generally for power transistors or other power devices. But adding a heat sink Will help to keep the device cool. In your case, Q1 is dissipating only about 67mW which is safely below the max power rating of 625mW and no heatsinl required. The second transistor is dissipating about 200mW. This too is more than half lower than max power rating which is good an wont require heatsink. Note though that these are DC power though and the overall power (DC +AC) must be lower than max power. Take a look at peak power of Q2 when ac signal is applied at input of your circuit. It should be well below Pmax. 

To determine if heatsink is require you need to check if Junction temperature of transistor is below a max of 150C . At this temperature the decide will be destroyed. Though a better temperature is 100C. If at your power dissipation the junction temperature reaches 100C then you require a heatsink. The formula for junction temperature is shown below.