A thermostat will always make a heat source output the correct amount of heat (providing that the probe is in the right place) but isn't necessary for overhead heat sources.

I personally would use a thermostat just for the peace of mind. A $30 Hudrofarm would be perfect.

If not I would strongly reccommend that you use a lamp dimmer so you have some control over the heat.

As for probe placement:

You could hot glue it to the back wall of the cage

You could attach it to the bottom of the cage (depends on what substrate you use)

You could dangle the cord

You could build a support frame out of PVC like this: