Lets say I have a pressure transducer sitting at the bottom of an open-topped 5-gallon bucket (assume its a vertical-walled cylinder). The transducer is measuring the gage pressure of the water column.

If the temperature of the water fluctuates (assume uniformly throughout volume, no evaporation) will I see a corresponding fluctuation in the output of the pressure transducer?

I understand that pressure is P=rhogh, so pressure is proportional to density, which changes with temperature. But volume is also proportional do density for a fixed mass, so I think that with a vertical walled cylinder, where h is proportional to volume, the measured pressure will not change because the increase in h will compensate for the proportional decrease in rho. Is this correct? If I had, say a conical vessel, would the answer be different?

Lets say I have a pressure transducer sitting at the bottom of an open-topped 5-gallon bucket (assume its a vertical-walled cylinder). The transducer is measuring the gage pressure of the water column.

If the temperature of the water fluctuates (assume uniformly throughout volume, no evaporation) will I see a corresponding fluctuation in the output of the pressure transducer?

I understand that pressure is $p=\rho g h$, so pressure is proportional to density, which changes with temperature. But volume is also proportional do density for a fixed mass, so I think that with a vertical walled cylinder, where $h$ is proportional to volume, the measured pressure will not change because the increase in $h$ will compensate for the proportional decrease in $\rho$. Is this correct? If I had, say a conical vessel, would the answer be different?