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.
As altitude increase pressure drops and TAS increases. This is because there is less air to put up resistance against the aircraft moving forward so the aircraft moves faster through the air. Concord could take adventage of this phenomenan all the way to 60.000ft because of special design allowing it to fly above Mach speeds. Most jets fly below Mach speed so they can not continue to fly higher. To check how altitude affect TAS here is a link to E6B calculator where you can input different altitudes and see difference in TAS:
E6B Emulator Its the last function on that page.
Of course temp also plays a role in this equation but its secondery at best and applies more to Mach definition then to inrease in TAS with altitude.
Any increase in temp or alt will increase TAS but TAS mainly increases due to pressure.