What kind of thermometer are you using? A digital thermometer with a probe is best or a infared temp gun, a good probe thermometer is an acurite 00891. What kind of heat bulb are you using? Is it red or blue? If not then switch to red or blue or your snake will be come very stressed.. If the temp in the room your snake is kept in is more than 75 degrees you do not need the heat lamp, if it is below 75 then put heat lamp on cool side. Your heat mat temp needs to be measured with a digital probe thermometer or temp gun and you need to check the temp under the substrate (bedding) right on the floor of the tub over the heat mat and make sure it gets no hotter than 94. Reason you check temp under substrate is bc snakes will burrow and a burn will eventually happen if the temp is not in the safe zone. For your heat lamp (if you need to use it) you need to check the temp of the hottest spot it touches and make sure it is in the safe zone, 88-92 is best but I would keep it closer to 88 for a younger snake. How is your heat lamp setup? You said you have a tub so do you have the heat lamp inside the tub? If so remove it immediately. Imo The only way you can really use the heat lamp with a tub is if you made a home made lid since the plastic lid can melt especially if your using it to heat your hot side. I've heard of people using them on cool side to heat the cool side to around 80 but if your cool side is below 75 a heat mat for the cool side would be safer than a bulb IMO. The thermostat your using that shuts off your heat sources when it reaches temp is fine but since your using 2 different types of heat sources that heat in different ways with different wattage you cannot have them plugged into the same thermostat, you need one thermostat for each heat source.
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