I agree with Spaniard. You pretty much have it backwards. A thermostat does account for fluctuations in air temp because it keeps the temp constant, not the power output. A dimmer keeps the power output constant, but if the ambient temp changes, so does the temp on the tape/in the tub.
Also, more or less, the temp of the tape is the temp of the tub...your interpretation of how that works was a little confusing to me too.
All in all, if your room temps are stable, you can get by with a dimmer. If not, or there are drafts, etc...you should get a thermostat. Thermostats offer peace of mind also, which is worth more than you may think.
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