This is good question in the field of semen biology. yes, it could be done immediately. however regarding the acceptable fertility , it is main goal in Artificial insemination application. Since semen quality is already known , if the precautionary measure along with good health of animal to be inseminated would certainly result in successful conception.
As far as my experience, you should do as soon as possible. However, if you have no chance to inseminate within immediately, you could do insemination within 6 hours (in any time points 0-1-2-3-4-5-6 hours). After 6 hours is a critical time point for sperm quality parameters which abruptly decreases at 5 C.
important thing is u should adjust the semen's thawing rate then keep it warm at more 32 degrees. Insemination can be within a hour, not more than 1 hour. sorry. it is my experience!
After warming/thawing.....insemination with frozen semen sample should be performed within 30 minutes for best results.
As over exposure of frozen sample to ambient environment can lead to decline of sperm motility, blockade of sperm capacitation and even viability & survival. Which is suboptimal and expected results would be lower.
Normally, two things that act together must be taken into account. One is the heating velocity and its rate (speed vs. time). The other is the diluent used. It is clear that as time passes the semen quality and its alleged fertility will decrease, but both factors can act by increasing or decreasing its viability. The other issue to consider is the time in which the semen was kept at 4-5 ° C and the cooling curve performed, especially when passed the critical temperature of 15 ° C.
After warming the semen, you must inseminate it as soon as possible! Keep in mind that, the sperm needs around an extra 6 hours to reach the oocyte in the female reproductive tract. thus, every minute after cooling or/and warming is very valuable!
You can keep your semen in 5 degrees C and prepare everything you need for insemination (especially the ewes), then start to warming and insemination.
I think you talk about frozen ram semen... If you use thawed sperm, you should carry out your artificial insemination as soon as possible (It is not exact however you can check this with thermoresistant test after thawing. You can check motiity until 1 hours or more because every frozen semen have different thermoresistance even if same ram may be used). It is harmful effect of re-cooling or re-frezing of semen on sperm paratmeters. It's mean that your conception rates will be decreased shrarply if you use this semen.
If you talk about chiling of ram semen, there are alot of dependence and variables (condition of ram semen (individuality), extender you use, storage condition (some times cooler may not be good), moreover you need extra protective agents like glycerol (yes cryoprotectants some times needed for short term storage it is not exact), ambiant temperature etc.) affecting success of storage. Nevertheless 1 or 2 days is ideal for this aim. Sometimes 3 days stored semen can be efficiently used. Dont forget, check the motility before artificial insemination to be sure motility and viablity of short term stored semen. Some times unexpected stiuations occurs.
I hope this short information help you. Good luck,