  This article is dedicated to insensitization issues of a quadratic functional
involving the solution of the linear heat equation with respect to domains
variations. This work can be seen as a continuation of [P. Lissy, Y. Privat,
and Y. Simpor\'e. Insensitizing control for linear and semi-linear heat
equations with partially unknown domain. ESAIM Control Optim. Calc. Var.,
25:Art. 50, 21, 2019], insofar as we generalize several of the results it
contains and investigate new related properties. In our framework, we consider
boundary variations of the spatial domain on which the solution of the PDE is
defined at each time, and investigate three main issues: (i) approximate
insensitization, (ii) approximate insensitization combined with an exact
insensitization for a finite-dimensional subspace, and (iii) exact
insensitization. We provide positive answers to questions (i) and (ii) and
partial results to question (iii).
