How might temperature affect gene expression in an organism?

Yes a gene's expression CAN BE ALTERED BY TEMPERATURE. Yeast are a simple example of the basic eukaryotic cell , thus are models for the basic animal cell. Any functions in yeast cells most likely are evolutionaly  conserved in higher animal cells. Temperature dependent gene expression is studied a lot in Yeast cells. They have protective genes that express what are called Heat Shock proteins.

Human cells undergo differential gene expression after thermal injury and certain cells produce different proteins at different temperatures.

here is an example of the turtle sex gene determinations:

Evolution of the gene network underlying gonadogenesis in turtles with temperature-dependent and genotypic sex determination
Nicole Valenzuela1
Department of Ecology, Evolution and Organismal Biology, Iowa State University, 253 Bessey Hall, Ames, IA 50011, USA

Correspondence: 1Email: nvalenzu@iastate.edu

Your body has heat receptors on all of its cells.  When the temperature of your body increases, expression of certain genes changes.  We all have proteins called Heat Shock Proteins (HSP).  If our bodies get too hot, heat shock proteins are expressed in order to try and salvage certain proteins that can't tolerate the heat.  The problem with an increase in temperature, is that the heat is able to denature (permanently damage) many proteins.  It is not really a change in expression of genes that would affect the offspring, but rather severe protein damage.  If our body temperature changed from 98.6 to 101, we feel incredibly uncomfortable.  If our body temperature permanently changed from 98.6 to 101, we would develop a large build up of cellular damage.  Since, alligators and turtles are cold blooded, the environment regulates their body temperature.  If the environment warms up, then the alligators and turtles bodies warm up leading to cellular damage.  This damage greatly affects reproduction and organismal well being.

The hypotheses
a.Rate of growth of embryos is dependent
on incubation temperature.
b.Beginning and end of thermo-sensitive
period of development for sexual
differentiation is defined by the
embryonic stage of embryo which is
strongly correlated with its mass.
c.Estradiol is the feminizing hormone in the
gonad. Content of this hormone in the
gonad is strongly correlated with the
aromatase activity in the gonad.
d.Aromatase activity is very low at
masculinazing temperature and increases
strongly at feminizing temperature.
e.Growth of the gonad follows the growth
of the sharing individual but growth is
inhibited by estradiol present in the
gonad.
f.Sexual phenotype is dependent on the
quantity of estradiol (measured here by
the activity of aromatase enzyme) per
unit of gonad.

http://www.seaturtle.org/ists/PDF/final/2551.pdf