On to myfolsom.com to check out recs for HVAC folk (where else would we go?).
So, here's my advice (and sad news): Check the contractor license info, and you'll find that most of the companies that have been recommended here in the past have suspended licenses and/or no bonds.

Here are a few samples:
Alley & Co, #675403: License and bond are active. However, two disciplinary actions are pending (one each in the form of a "citation" and "accusation").
Alex, from Galex Heating, #824764: License is suspended for failure to comply with an oustanding civil judgment, and under "Contractors Bond Suspension".
Jim Thomson, Thomson Mechanical, #582459 : License is suspended for failure to resolve an oustanding final liability from the FTB, and under "Contractors Bond Suspension".
Now I realize that these things happen as part of doing business, but we feel more comfortable going with someone who currently has a "clean" record. We called Rick (Richard) White, of the Air Company. Unfortunately he doesn't do out-of-warranty repairs. Fortunately, he did have someone he recommended:
David Rogers, #585643: Current license and bond, no issues pending. We called him, liked him, set up an appointment. He came on time (called first to let us know he was leaving his previous appointment), and our heater is now working. We paid only the minimum trip charge (which isn't so minimum these days, but it was similar to others we had called). Based on his bonding history, he has over 18 years of experience. (And based on watching him work, he certainly knows what he's doing.) Highly recommended!