All liquids are thermoresposnive, usually decreasing in density with increasing temperature [pure water (not sea water) between 0 degrees C and 4 degrees C is a rare exception, increasing in density with increasing temperature]. Thus any liquid that is immiscible with water will work. Most hydrocarbon liquids are immiscible with water, as is mercury (but mercury is highly toxic, much more so than most if not all hydrocarbons).

The cheapest and most commonly available termo-responsive liquid  I know (that would not mix with water) is cooking oil.

Another way to avoid the first liquid mixing with the water in the other reservoir is to insert a small plug of mercury in the horizontal tube connecting the two reservoir. In this case, the first liquid can be water (perhaps coloured water). This set-up would minimize any non-thermal effect due to the possible different density of the two liquids.

 I do not follow what you want to achieve: Is it a thermometer with 2 liquids?

Also what range of temperatures you are interested in?.

In general the solubility is the first factor but you need to also consider viscosity of the thermo-liquid and interfacial tension between them (capillary forces in the connection between reservoirs. Note that Mercury is thermo-responsive

A variation of Roberto's suggestion  is to have 2  vertical reservoirs with water at the top while  the bottom part+ connection filled with a denser fluid (e.g. a chlorinated hydrocarbon). In this case the response need to be calibrated as both fluids will expand.

In general the solubility is the first factor but you need to also  consider viscosity of the thermo-liquid and interfacial tension between them (capillary forces in the connection between reservoirs.