If you have a good thermostat (one with safety relays/good programing... basically anything in the herpstat line) the chances of a burn are extremely low... cheap thermostats that don't have any safety features are still safe to use but not completely bullet proof.
If you can achieve proper humidity levels then I would say just stick with heat lamps, there is nothing wrong with them.
If you aren't using a heat source under the cage, then I would put the thermometer probe on the surface of the substrate... the substrate could be lowering the reading (when it says 87 the surface might be more like 90-92... and when it says 90 it could be more like 95) it all depends on how thick the substrate layer is and what you are using. If the thermometer probe gets moved around some it doesn't really matter... it isn't like the thermometer is regulating a heat source, just make sure it is in the right place when taking measurements.