There is another thread on this board which misapplied the pressure-temperature formulas. Here's a better explanation of the formulas which can better back what Bill Belichick was explaining in his press conference yesterday AND why the Colts' footballs wouldn't need to similarly be below the standards.
Belichick mentioned that the rubbing preparation process they use -- in retrospect -- provides an artificially higher pressure of 1 psi. (Mechanical energy converted into heat.) How high a temperature is needed to go from 11.5 psi (at say, 70 F) to 12.5 psi?
Making an assumption that the change in volume is small, we can use T2 = T1*P2/P1. The critical detail overlooked in the other thread is that not only do you need to use Kelvin temperature, but you need to use absolute pressure. To convert from gauge pressure (psig) to absolute pressure (psia) you need to add the atmospheric pressure (typically 14.7 psi): psia = psig + 14.7.
Answer: you only need to get to 90 F internal temp.
To complete the rest of the argument, either: a) the balls delivered to the referees were measured soon thereafter while the interior of the footballs were still warm,still at 12.5 psi, and left unchanged, or b) the balls had reached room temperature, and that 11.5 psi, 70 F balls received a cursory inspection, felt fine, and were not inflated by the referees back to 12.5 psi.
The ball pressures were then measured at halftime after being outside at 50-51 F. If the balls had reached this new equilibrium temperature, the new pressure would be 10.5 - 10.6 psi.
So, what about the Colts' footballs? Let's assume that they did not do the same rubbing process as the Patriots, and furthermore target the high range of the allowed pressure. Their footballs would start at 13.5 psi and 70 F. Cooling down to 50 - 51 F would result in 12.4 - 12.5 psi.
There are other details (barometric pressure change contributions could contribute a few 0.1's of a psi, contributions from small volume changes, and knowing what the actual interior ball temperatures were at the time of measurement) but the preceding description shows how the Patriots' footballs could measure 2 psi below the low end of the standard at halftime while the Colts footballs were just within the standard.