Some very specialized projects may require on site work by the consultant, but these are exceptions. Temporary agencies want to place people at your site, usually full time for the duration of the project. More often than not you will be paying for more hours than you need. Temporary employees rapidly become a part of your organization and begin to see problems and solutions in the same terms as your own people. This may feel good, but robs you of your consultant's objectivity.
Consultants work with management to determine the real problems and to develop solutions.
The very process presumes an active engagement of management with the outside advisor. Temporary agencies appeal to those who want to turn it all over to someone else. This is fine if the project is catching up back orders, or ending backlog in the file room. It's disastrous when new policies and programs are being developed. Most consultants have pagers or cell phones that will allow you to reach them wherever they are.