A temporary (aka interim order) is one made by the court at a motion. This usually is based upon the judge reading the written evidence given by the parties through affidavits and listening to the arguments made by the parties lawyers. These temporary orders last until they are replaced by a final order of the court or some other final resolution of the matter between the parties.
A final order almost always is a result of a trial or the consent of the parties. At times it can arise from a legal shortcut such as a motion for summary judgment.
The main difference between a temporary and final order is that the final order is made after what is supposed to have been a careful deliberation and evidence on all of the facts which is why it usually arrives either from the final settlement or the conclusion of a trial. A temporary order is exactly that, a temporary agreement or order made by a motions judge to deal with temporary issues until the court can make a final decision. An example of a temporary order would be temporary custody and access to the children until there is a final settlement or decision on this point. Another example would be the amount of child or spousal support that would be paid until the matter was finally determined by way of trial or settlement.
A without prejudice order is one in which the parties have agreed to or at times the court imposes simply a patch work temporary solution without establishing a precedent. An example would be, the parties cannot agree on the income that each of them earn and so as not to establish a baseline or any kind of a decision on the point the court, or the parties themselves might agree that on a without prejudice basis and until further evidence can be obtained or the parties are prepared to litigate the matter that each of the parties incomes is deemed to be X and Y and from that starting point, support can be ordered.
Another example of a without prejudice temporary order might be one granting either the mother or father temporary custody of the child/children just so that there is a home base and so as to temporarily and without setting a status quo settling the issue.