How to keep insects away
I've had problems with insects, even when I lived in a relatively cool place.  (My apartment was next to the trash chute, and on the day they sprayed for bugs, it would drive them into my place for the better part of a week).

To help prevent long-term visitors, you want to remove sources of food.  A big one is areas of moisture, which start creating small bits of mold that the insects feast on.  Make sure you don't have water dripping below your sink and if you have a shower, leave the curtain and door or window open to let it vent after every shower.

To keep away the random explorers (or to deal with existing problems), I really like glue boards.  They're just a rectangle of cardboard with a really stick substance on one side.  You can either just peel off the protective paper and set them in places the insects typically visit (under sinks, behind toilets, basements, etc), but you can also typically fold them into a tent-like triangle or an open-ended box that you can place on countertops or floors.  (always place them tight up against the walls, so the open sides are accessible)

Glue traps will catch most insects (even flying, if you can get them to land on them.  Some are 'peanut butter scented' as a lure) and mice.

A few bits of warning, though:


Make sure you put them where you're not going to step on them.  They will stick to your shoe.  If you're not putting them under tables or such, fold them into a tent.
If you have a lot of insects already, it can be pretty disturbing to see how many insects you actually had.  (I put them in my basement to deal with camel crickets, and it was basically filled.  And the insects were still moving, so it pulsed)
It's not a very humane trap for mice.  They get stuck and then keep struggling to get unstuck.