I'm designing a device which will use ultrasonic transducers in a way similar to sonars. Is it absolutely necessary to correct for the drift in the resonant frequency due to temperature fluctuations? How much will the performance of my system decrease should I choose not to to this? How would I even get around doing it?
First, generally your transducer is usually in close proximity to your receiving unit (or if they are one and the same). Thus, any change in resonance is likely to occur on both elements at the same time, so it won't affect their send/receive performance. Secondly, the speed of sound in air depends on density and thus temperature, so you may want to take this into consideration. Thirdly, all of this depends entirely on the level of accuracy you require. If you environment is not going to be shifting temperature that much, you can probably get by with estimates based on a median temperature for your environment.
A link to your transducers would help. The ultrasonic transducers that I've used had a fairly broad resonance. One with a nominal center frequency of (say) 4 MHz might be 2 MHz wide. So no temperature changes were observed (or expected.) These were used in single pulse mode. (A single sine wave period.) And so needed to be broadband. Else the single pulse would have caused them to ring for a long time.