Required by law. Ontario law requires this credential for the work. A contractor without it cannot legally do the job, whatever the quote says. Technical Standards and Safety Act, 2000, O. Reg. 215/01 (Fuel Industry Certificates).
This work usually needs a municipal permit. Unpermitted work has to be disclosed when you sell, and an insurer can decline a claim arising from it.
Ask before you hire
What is your TSSA certification number for the gas work?
Did you perform a heat loss calculation, or are you sizing by rule of thumb?
Is this equipment owned outright, or is any part of it a rental contract?
Are there current rebates for a heat pump, and will you file for them?
What is covered by the labour warranty, and for how long?
An oversized furnace short-cycles, costs more to run and wears out sooner. Ask for the heat loss calculation.
You asked for the trade Heating and cooling, and the words "caulking", and businesses serving Toronto. Of the 12 businesses listed, none match every one of those.
The cost band and the licence requirements above still apply. They are what you need to judge a quote from anywhere else: whether the price is in the range, and whether the person quoting is allowed to do the work at all.
Listings here are seed data for demonstration and are labelled as such on each profile. Cost bands are what GTA homeowners are typically quoted, not offers. Always confirm a licence number against the issuing registry yourself before work starts.