The Ehow link is incomplete. If you don't have the recipient's TIN, you are required to withhold 28% for taxes and include that on the 1099-MISC. You have to boost the amount paid to cover the tax (divide by .72 to get the correct total) and report that as non-employee compensation in box 7 and then show the 28% for taxes in box 4. You must remit that 28% to the IRS.
There are several other things to keep in mind. If the installer is a corporation, a 1099 is not required. You should send him a Form W-9 and ask him to complete it and return it. If he claims to be a corporation then you don't prepare a 1099-MISC. If he refuses to submit the W-9, you proceed as noted above.
Copies of paid checks are not sufficient. You need to substantiate the expense with invoices, paid receipts, etc. They must clearly detail what was done, when it was done, and the total cost.
An HVAC installation is a capital improvement. It becomes part of the property and is depreciated on the same schedule as the property is -- 27.5 years for residential and 39 years for commercial. You can expense any unclaimed depreciation at disposal time when the system is replaced if it lasts less than that number of years.
For future reference, always insist on a completed Form W-9 before making ANY payment. No W-9 = no payment. No exceptions. That is enough to motivate most to comply with the law. Also insist on a signed contract that outlines all work to be done and a firm price quote up front. Again, no contract = no payment. No exceptions. If there are any contract mods or up-charges, these must be documented. Finally, no payment without a detailed invoice. No invoice = no payment. No exceptions. This applies to any initial deposit, any progress payments, and the final payment.