To get a 10% pressure change, (to make it easy, start at 27C or 300K (close enough to absolute for this)), the temp needs to go up by 30 degrees, (C & K degrees are the same, unlike Fahrenheight), so the tyre is now at 57C.
Actually, I was thinking about it afterwards & I got it wrong. It should be as follows:
PV~T so:
V~T/P and if the volume is constant
T1/P1 = T2/P2 so
P2 = T2*P1/T1
P2 = 244*300/300 therefore
P2 = 244psi down from 300
or if it was 200 to start with
P2 = 162.67 psi
My bad!
edit: Forgot to add the 14.7 for assumed vacuum at altitude!
So P2 = 162.67 + 14.7 = 177.37psi