Overestimating the initial introduction to the business as being sufficient enough to getting the prospect excited and participative is definitely something that should not be condoned.
This may even be seen as a rather poor business judgment on the part of the introducer. The exercise of following up on the initial introduction will give the individual an idea of how the first contact was viewed and whether the time is right to push further for a firmer commitment to the business.
The interval would also have given the prospect an ideal amount of time to mull over the business idea and be ready with questions of their own, thus if there is no follow up sessions forthcoming the interested party may seek other alternatives.
The follow up contact should also be done in a friendly yet professional style, which may include staying focused on the business topic rather than discussing a variety of other topics that would waste valuable time.
As the initial contact may have lacked the opportunity to get into an in-depth detailed discussion about the business, the follow up session would be the perfect time to indulge a little more into this area.
Providing relevant material that are highly convincing in nature would also be something worth considering at this follow up point.
Asking for referrals could also be included in the follow up contact with the warm market target audience. This would give the impression of being very serious and focused about the intention to make a success of the business.