This depends very strongly on what kind of oven you have. Since there are many, many variations in oven design, I'm going to go over three contrary options based on my own personal experience.
Gas oven, freestanding and thinly insulated: with an oven like this, you can turn the heat down to a lower temperature, put the new food in, and expect that the new food won't cook a lot differently than it would if you allowed 10-15minutes for the oven to cool. Gas ovens depend heavily on hot air convection from the gas flames to transfer heat to the food, and when you turn down the temperature, if the oven is not well-insulated, the temperature will fall almost as quickly as the food heats up. The only food I wouldn't do this with would be something which was very sensitive to rapid overcooking.
Electric oven, built-in and well-insulated: my current electric oven, on the other hand, is very well insulated and relies on radiant heat from the walls of the oven to cook foods. As such, if I turn it down from 450F to 250F, I can expect that foods inside the oven will still be exposed to heat higher than 300F for at least 1/2 hour. As such, if I need to drop the oven temperature for cooking reasons, I prop the oven door open.
High-end electric oven with exhaust fan: I've also had the chance to cook in higher quality ovens that contain an internal exhaust fan with an exhaust pipe to the outside. These ovens actively cool themselves off when you lower the temperature, so going from 450F to 250F would take less than 10 minutes, despite the thick insulation. With this oven, you just turn the heat down and put the food in.