So by placing the probe directly on the heat tape, how often does your thermostat turn on and off? Depending on ambient temp of the room, the thermostat could be flickering on and off at a high rate. Flickering on and off of thermostats can cause failure by over working them. i've seen many cheaper thermostats that fail in the "on" position. When this happens, your heat tape runs at full voltage, it is now unregulated and uncontrolled. I have a friend who had exactly this happen to the point he fried the snake. Yes it died.

Dimmer switches can fail. If they fail, the circuit is interrupted and power is then lost. No shorts to worry about. So worst scenario, the snake falls to room temperature if setup my way. Do it the other way, thermostat fails in "on" position, flexwatt overheats,and fire occurs. Not worth the risk over lacking the use of a dimmer switch.