I'm guessing you want to use a strain guage instead.
Still, this has several problems. Finding/building a suitable weight, keeping said weight +string sanitized, attaching to the strain guage and somehow pass through the lid of the fermenter in a sanitary way.
After that you just need to worry about CO2, krausen and drift of the strain guage to mess with the measurements, before you're done.
That's why you don't just do that.
Not saying it can't be done (it even has been done with the beer bug I think), I'm saying it is not all that easy and probably more trouble than the reward.
Strain gauge is what I meant - long day.

I tend to not really want to worry that much and make fermentation temperature changes based on visual observation or set times which tends to work just fine.