DovidBT,
“Can tefillin that’s kept in a car get damaged due to hot temperatures during the daytime?”
Most definitely. Heat is one of the worst things for tefillin.
“Does placing them in an insulated container avoid or reduce the problem?”
It can, if the insulation is sufficient to keep the temperature inside the container down.
“If an ice pack is also in the container, will that make it worse by causing condensation?”
An ice pack might be a good idea, but the tefillin should be contained in a waterproof bag so the ice pack stays separate.