Energy profile of cyclohexene conformations
I found the answer in the book: "Practical Aspects of Computational Chemistry"
. In chapter 19: Unusual Properties of Usual Molecules. Conformational Analysis of Cyclohexene, Its Derivatives and Heterocyclic Analogues.

The value for ring inversion of cyclohexene is smaller than the one of cyclohexane (which is near 10 kcal/mol):


  Value of ring inversion barrier is within 4.2–
  7.9 kcal/mol for molecular mechanics and 5.2–6.6 kcal/mol for quantum chemical
  methods.


The inversion proceeds as follows:


  The ring inversion process in cyclohexene includes three stage. The first
  stage involves the transition from an equilibrium half-chair conformation to a twist-boat conformation with a significant increase in energy. The second stage
  may be described as a very easy transformation of one twist-boat conformation to
  another via boat almost without any changes in energy. The third stage includes the
  transition from a twist-boat conformation to a half-chair conformation accompanied
  by a significant decrease in energy. The difference in energy between the twist-boat and the boat
  conformation is less than 0.01 kcal/mol. The boat conformation
  is just central point of this plateau and it is only the most convenient point for a description of the saddle point for the ring inversion
  .


The interconversion diagram should be something like this: