I think I wrote an article pertaining to that topic but I'm not sure how relatable it is.
Most of my thermocline work has been done in the great lakes where there is a VAST break and tempurature difference. In a lot of instances, we use thermoclines there just as you would structure in most other bodies of water.
Thermocline in the great lakes is most often effected by wind direction and wave action than anything else. You can have mid July days with a south wind that brings up really warm surface water. The fish will scatter (salmonoid species) as they just cannot stand that tempurature. You concentrate on tempurature breaks to find fish. When the North Winds blow, it will start to mix the cold and warm water and develope those thermoclines. We are not talking little ones in some lakes that can be in a hole or on the edges of streams. We are talking break lines that extend down 40 feet and might run 15 miles!
I suspect that pressure "could" push those break lines down with high pressure and bring them up with low pressure. More than anything, we look for winds to change our thermoclines more than pressure. Again, not really sure how relatable it would be to really small bodies of water (compared to Lake Michigan that is)!