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.

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