The problem occurs when cacti that have to be pollinated do not flower simultaneously. That means the pollen should be preserved somehow.
After about 8 hours of its exposure to the sunlight, the germinating capacity of the pollen decreases significantly. The stale pollen is even more susceptible to the sunlight. The negative effect of the sunlight may be explained by the pollen's sensitivity to UV rays. Therefore the pollen should always be kept in a dark place.
Temperature is not that crucial. However, it should be low if possible. I found the temperature of 5 - 10 єC favorable. Temperature below zero centigrade will do no harm either. So, you'd better keep the pollen in a cold room or in a fridge. At any temperature try to keep the humidity low. You can use a desiccator with silica gel or calcium hydrate.
The question is how long the pollen can be preserved? For instance, the pollination of Mammillaria theresae after 5 days was successful but it failed after 8 days. I also made experiments with Lobivia polaskiana. It was successful after 7 days of preservation. For other species of Lobivia the maximum timing lays within 8-12 days. I didn't try pollinating at later times.
The best method is to extract stamens from the flower and place them into a test tube filled with paraffin by 80% of its volume. Cork up the test tube and place it into the dessicator or a jar. You can keep the dessicator at the corresponding temperature. Instead of dessicator you can use a glass jar with a tight lid. Put some silica gel on the bottom and put a net rack above it. You can buy silica gel at a drugstore. Place the test tubes on the rack and cover the dessicator lid tightly. You can preserve the pollen for a year or more this way. Though you should make tests for each species.
