So according to you I should fly next to ground where temperature is highest and TAS "in theory" should also increase.....

I shell remember that next time I fly my little sexy sport car
Ok, lets be serious here.
I was being serious. TAS is higher near the ground for a given Mach number, but of course there is no point flying that low as you are likely to pull your wings off before you would reach any worth while Mach number. If you look at any of the Boeing manuals it says that TAS changes by approximately 1 knot for every 1 degree above or below ISA.
I'm sure your citation manual has this as well......