Temperature

When spreading granular fertiliser, you generally don’t need to consider temperature, provided the plants are dry. Otherwise, leaf burn may occur. Leaf burn can be prevented by spreading/spraying only when the crop is dry. You can check this by looking at various places in a plot to see if the crop is moist.
In general, you do need to consider temperature when applying liquid fertilisers. It should not be too hot and/or sunny, as this can cause leaf burn.
It is better to spray liquid fertilisers towards the evening when the sun is less bright.
Crop damage due to spreading/spraying is less likely in the spring than later in the season. Almost no damage occurs in late summer and autumn, as plants are more hardened off by then.

Sources:
AgroWeerAdvies, 2013.
Bouma, Agrometeorologisch specialist bij Agrometeorologisch Adviesbureau Erno Bouma, 2014