repeatedly turning an incandescent light bulb on and off every 20 seconds will cause damage to the bulb?
I'm not sure this is so mich an "original" answer as a combination/explanation/redinement of the other 2 already posted answers, but I'll try to help a bit.


As transistor pointed out in the question comments, the 'bulb'-life impact of rapid switching on several varieties of lights is discussed in some detail in If I flick the light switch on and off will it damage the light?
Autistic, Rothloup, and 2 posters in the other thread are all right about 'dimming' the incandescent greatly improving bulb life.  


I would recommend using an inductor in SMPS buck-converter arrangement as likely being the most efficient (be careful though, the efficiency of that one inductor could surprise you, incandescents have a very non-linear response &amp; tend to respond well to under-voltage drive).  
While the buck converter could arguably be run on from non-rectified ac current, I would personally recommend using rectified &amp; conditioned/smoothed DC (for predictable performance), and a pwm management that never cycles slower that 40KHz (so you don't have to hear it 'sing').

You should definitely replace the relay with solid-state components.  


At the least, a triac or optoisolator/'solid state relay' can switch your load faster than a mec. relay &amp; love longer.
Better by far would be using a bridge rectifier &amp; a capacitor to convert your input to smoothed/conditioned DC, then use a power MOSFET (if you get a 'logic-level drive' one, it won't even need any external buffering transistors) to run the aforementioned buck converter.

Putting it all together, if you PWM a buck converter, with solid-state switchgear, to keep the light somewhere between 'just warm' and 'hot, but barely glowing,' you should be able to maximize your energy efficiency, component lifetime, and the precision/stability of your incubator's temperature control.