The payment schedule is a term of your contract, not an administrative afterthought, and it is where a surprising amount of your protection lives.
Ontario's guidance for home renovations and repairs sets out what a contract must contain, and the list reads like a checklist for exactly this job: the contractor's name and contact information, a thorough description of the work and materials, a clear description of any warranties, the total cost and terms of payment, a work schedule with start and completion dates, a payment schedule including the deposit amount, responsibility for clean-up, and — the line that matters most on a furnace job — all sub-trades that will be contracted out and who will pay for them. The same guidance recommends keeping down payments to no more than ten percent, advises never paying in full before the work is done, and states the principle that should govern how you read your quote: if something is not written in your contract, you may not get it.
That page also carries the single most actionable sentence in this article, and it concerns the estimate. Under Ontario law the final price cannot exceed the original estimate by more than ten percent unless you have agreed to new work or a new price — but the protection depends on something you have to do. The estimate must be incorporated into the contract. An estimate that sits outside the agreement, as a separate quotation you were emailed and never referenced again, carries no ceiling at all.
Provincial variation here is sharper than most people expect, and it does not run the way you would guess. Alberta caps the same overrun at ten percent to a maximum of one hundred dollars, which on a nine-thousand-dollar furnace job is dramatically tighter than Ontario's percentage. Quebec's fixed-price rule holds the agreed price even where the terms of performance change. Saskatchewan uses a qualitative test rather than a number, asking whether the final charge is substantially higher than the estimate.
Saskatchewan does, however, publish the clearest deposit rule in the country. Its Financial and Consumer Affairs Authority states that direct sellers of home renovation products or services "are prohibited from requiring a consumer to pay more than 15 per cent of the total contract price" until the ten-day cancellation period has expired. British Columbia caps a direct sales contract down payment at the lesser of one hundred dollars or ten percent. Quebec goes furthest, barring an itinerant merchant from taking any payment — or performing the installation — before the cancellation period ends. Ontario and Alberta have no statutory ceiling on home services, which makes Ontario's ten-percent recommendation the practical benchmark there.