I have a temp controlled hot air gun, but most of the time, I use a gas soldering torch with a hot air attachment. The actual one I got was from Aldi so it probably cost $20-$30 - I doubt I would have paid more.
With the hot air attachment, there is no flame at the nozzle. It is near instantaneous, it is compact so I can move it around the wire easily, it needs no electricity, and the torch can also solder so it is great for quick field repairs.
The maximum air temp from the hot air nozzle of the torch is 500 degC, but is is easy to turn the gas down for 350 degC at the nozzle and 130degC at a distance of 2cm. By regulating the distance of the torch from the heatshrink, there is no risk burning of wires or heatshrink.
The temperatures needed to shrink heatshrink goes from about 90degC for polyolefin, 100 deg for PVC up to 250 degC for Teflon TFE.
I have also used the very cheap "Gas Soldering Pencil Torch" that you can get on ebay for $3 inc postage, but they do have a significant flame, they have no igniter and the gas flow control is very erratic.