To fill in some of the gaps:
The pressure it takes to have a passenger car tire explode is over 100 psi - unless it is damaged.
The inflation pressure specified by vehicle manufacturers (on the vehicle tire placard) for cars is 35 psi or less (with a few exceptions.)
When referring to cold tire pressures, it ALWAYS means ambient conditions.
Yes, the pressure will change with the outside temperature, but within the same day, it doesn't change enough to worry about.
Yes, a tire generates heat and that affects the inflation pressure. The rule of thumb is no more than 10% - so we are talking 3 psi for a car.
The max pressure listed on the sidewall of a tire is exactly that - a maximum (and there are a few exceptions). Do not use that value for anything else.