I am going to make a quick bread recipe that calls for an 8" X 4.5" (20 cm X 11 cm) loaf pan, but I only have a 10" x 5" (25 cm X 13 cm) loaf pan.
I've done the calculations and know I need to increase my ingredients by 40%. But how much should I increase the oven temperature and cooking time? The recipe calls for 70 minutes at 375 °F (190 °C).
I agree with FuzzyChef's answer, though I'd emphasize in general that this is often a question as shape as well as volume. A cake that is increased in size but also baked in a wider pan so its overall thickness is about the same as the original may not need much additional cooking time at all, or the increase might be small. When one increases all dimensions (and thus increases the thickness too), it takes longer for heat to migrate to the center and thus may need a more substantial increase in cook time.
Also, I want to address the reference made to "increasing the oven temperature." Generally speaking, when making a larger cake or quick bread, you don't want to increase the oven temperature, as it may very well cause excessive browning on the exterior (or burning, along with perhaps drying out near the edges) before the center is cooked.
If anything, larger cakes and quickbreads sometimes call for decreasing the oven temperature, to allow extra time for the interior to cook before the exterior gets too brown. If the temperature is decreased, the time must be increased to take this into account. (FuzzyChef's linked document shows these trends too.)
Unfortunately, there's no general rule that applies in all cases, as some quick breads may be prone more to excessive browning, while others may be fine if baked a bit longer at the standard temperature. Sometimes adjustments in leavening or other ingredient adjustments may be necessary to take into account different time/temperature as well as to allow a structure that must rise higher.
My cooking club, several years ago, obtained a worksheet from a commercial manufacturer of cake pans, which I've just republished (I can't name the company, but I can share the data). As you can see from the sheet, when making white cake, an increase in volume of 50% results in an increase in cooking time of about 5 minutes, provided that you are not increasing the depth of the cake (just the length and width).
Since your quick bread is somewhat longer-cooking than white cake is, I'd think the increase could be up to 10 minutes. I'd suggest starting to check it at the time the smaller loaf would have been done, though, and to believe your toothpick over the timer.
