but this tends to support your position...but only at a very cold and specific temperature where the water would be almost frozen at the surface, and below 62 degrees below that and then around 39.16 degrees at the bottom.
This is of course preposterous but does occasionally happen resulting in some tremendous and quite unusual fish kills.
But to give some understanding to your 'feeling the temperature".
A body cannot register temperatures...only the degree to which heat is being lost or gained....the often given example is when people play in th esnow without gloves and come in and put their hands under 50 degree tapwater they swear the water is HOT.
Anecdotal information is misleading.
Density of water calculated from formula in 68th CRC Handbook of Chemistry and Physics 1987–1988. Density of water at 1 atm (101.325 kPa, 14.7 psi) (little or no difference at 100 kPa) TemperatureDensityCelsiusFahrenheitkg/m³ 32 °F 999.839523.98 39.16 °F 999.972015 59 °F 999.099616 2/3 62 °F 998.832220 68 °F 998.204125 77 °F 997.0449
as you can see water becomes more dense till it cools to 39.16F. At that point it becomes less dense as it starts to form crystals until the crystline network is near complete (ice).
But the middle water being cooler than the water above or below it....like I said, JG will be proud of you.