Preventing freezing pipes in well head
A "heat wrap thing" sounds like the cheese they sell at the big-box shops.  Cheap and ugly and not very good.  Take it back. 

The right way: good heat tape

First, use the good stuff.  It's called self-regulating heat tape , that is, it reduces its own power as temperature rises.  Effectively shuts off at 150F, which means you won't boil out your pipe if the thing goes crazy.  You probably want the highest wattage you can get, e.g. 10 watts per foot, and spiral it nice.  Obviously, get the 240V heat tape.   

McMaster shows the variety available. 

You'll need to make those electrical connections correctly for this wet location. 

If you want, you could put a thermostat on it.  240V thermostats are cheap and readily available, used for baseboard heaters.  Getting one fit for outdoor use might be trickier. 



After the pipe is wrapped with the heat tape, wrap both with foam pipe insulation.  You'd only want to do that with the "good" self-regulating heat tape.  Otherwise the insulation would only help the cheapie heat tape go into thermal runaway and set the insulation on fire. 

The wood housing lined with insulation is a good idea, probably better than the concrete top.  The light bulb was a silly way to do it, not least, the bulb will burn out and you'd never be wise. 

Try to keep water out of the area. Maybe make a weatherproof cover that goes over lid and walls.

Or maybe light bulbs after all

Here's an alternate way to approach the light bulb method. Install three incandescent lamp sockets.  Here's the tricky part: Wire all 3 sockets in series across the 240V.  Hot----lamp 1----lamp 2-----lamp 3----Hot.  Three matched bulbs in series will run 1/3 the voltage, or 80 volts.  So you can use common 120V bulbs.  And at the lower voltage, they'll burn exponentially longer.  But since they're in series, if one goes out, they all go out.   The bulbs will burn at slightly less than half their rated wattage.