If you can tolerate some temperature "ripple", a bang-bang
controller with LASCR or photocoupled TRIACS might do.
I doubt you need linear closed loop control, this hysteretic
scheme might do the job if +/- a couple of degrees is OK.
Is it necessary that all the power run through one switch?
If so then you need something like a 20A TRIAC / relay /
whatever for some safety margin on 220V power, or a
40-50A on 110V. But if you have strip heaters plastered
around a big can you could separate them and run more,
lower current switches perhaps, with common control.
There are lots of cheap temperature controllers on eBay
that could run relays or the opto inputs of isolated TRIACs.