I'm assuming your are using the BIAB method? I didn't see that mentioned anywhere.
A couple of suggestions:
- Use the strike temperature calculator on the Green Bay Rackers website
https://www.rackers.org/calcs.shtml
Just plug in your numbers and you'll hit your correct initial mash temperature every time.
Trying to bring the mash temperature up to the correct level using bottom heat is a hassle and will result in overshooting your mash temp, which you've already experienced.
-Go with a thinner mash, like 1.75 qt/lb. The more water water, the more thermal mass, the longer you can hold your temperature.
-Have a Gallon of boiling water in a side pot going. If for some reason you mess up your initial temperature, you can stir in boiling water to bring it up. Also, keep an eye on your temperature as the mash progresses, when it falls 3-5 degrees F, just stir in more boiling water to bring the temperature up. For me, this method works better than adding bottom heat. You can also use this method to perform step mashes. Use the Rest Calculator on the Green Bay Rackers website to determine how much boiling water to use. A 4 cup Pyrex cup comes in handy to measure and add the boiling water. Don't fuss too much with the temperature, if its off by a few degrees, your beer will be OK.
-As others have mentioned, insulate your kettle with an old coat or blankets. If your kettle has head space at the top, you can lay a piece of aluminum foil on top of the mash.
-Perform a test run with your stove. Is it gas or electric? My electric glass top range holds heat for a long time, is it better to move the pot off the burner or leave it there? If you heat a kettle of water to 165F and turn the burner off, does the temp keep rising or stay the same?
Try some different things and see what happens.
-When you get tired of temperature swings and spilling wort on the stove when you pull the bag out, go to Walmart and get a 5 gallon round cooler for about $20. You'll need to add a spigot and a 90 degree elbow for the inside of the cooler. You don't need a false bottom or anything else. Put your BIAB in the cooler and use that for mashing. Pre heat the cooler with tap water before mashing and you won't have to do anything for an hour, just put your grain and water in there and forget about it.
If you are short on space, the cooler can be used to store brewing equipment so it doesn't really take up any more space than you are currently using.
Happy brewing