Date: 201509
Local time of day: 0601-1200
Location: ZZZ.Airport, US
Flight conditions: VMC
Light: Daylight
Aircraft: B737-700
Flight phase: Taxi
Aircraft component: Pitot/Static Ice System
Component problem: Malfunctioning
Reporter organization: Air Carrier
Reporter function: Pilot Flying; Captain
Reporter qualification: Flight Crew Air Transport Pilot (ATP)
Human factors: Confusion; Troubleshooting; Communication Breakdown
Second reporter function: First Officer; Pilot Not Flying
Anomaly: Aircraft Equipment Problem Less Severe; Deviation / Discrepancy - Procedural Maintenance; Deviation / Discrepancy - Procedural MEL / CDL; Deviation / Discrepancy - Procedural Published Material / Policy
Detector: Automation Aircraft Other Automation; Person Flight Crew; Person Dispatch
When detected: In-flight; Taxi
Result: Flight Crew Diverted; Flight Crew Landed As Precaution; Flight Crew Took Evasive Action; General Maintenance Action
Contributing factors: Aircraft; Chart Or Publication; Manuals; Procedure
Primary problem: Aircraft

Narrative: After taxiing for takeoff; the First Officer noticed that the Captain's pitot light had illuminated on the overhead panel. I stopped the aircraft on the taxiway and set the parking brake. We advised Ground Control that we had a Maintenance issue and would get back with them.We ran the appropriate checklist and also noticed that the Captain's pitot circuit breaker behind my seat was popped. I gave the aircraft and communication duties to the First Officer and established a phone patch with Dispatch and Maintenance Control. Maintenance advised that we should not reset the circuit breaker and; with Dispatch concurrence; cleared us to continue to our destination under MEL XX-5-04. I completed the required logbook entry and placarding procedures. I had a lengthy discussion with Dispatch and Maintenance about the destination weather forecast; which was calling for 1;200 feet broken clouds and 10 miles visibility. The temperature at destination was 65 degrees and collectively we were all focused on avoiding icing conditions throughout the flight. We determined that the weather was clear to destination and that there was no icing conditions to be encountered. We ran all the appropriate checklists and; just prior to taxiing to the runway; the First Officer restated that the MEL in the performance manual stated that we were required to avoid icing conditions. I briefly glanced at it and we were both comfortable that the weather was good and the low cloud deck at XXX was well above freezing temperatures. We had clearance from Dispatch and Maintenance to continue as well. We were good to go.Enroute I received an ACARS from Dispatch. We had all overlooked Proviso B in the MEL; which stated the aircraft was dispatchable for 'day VMC' only. I remarked to my First Officer that I couldn't believe we had all missed that note in the MEL. He was growing concerned with the weather at XXX and Dispatch assigned an airport near our destination as our new alternate. I checked the weather for the new alternate and it was reporting scattered clouds with 10 miles visibility so elected to proceed to our destination and hold if needed until we could shoot a visual approach.After about 20 minutes in holding over our destination; it was apparent that a visual approach was not in the cards so we diverted without incident. The aircraft was fixed and; within an hour; the MEL was cleared and we proceeded back to our destination.  Throughout the entire flight; we never flew into IMC conditions.The bottom line is that I should have taken more time to review the entire MEL and all provisos associated with this mechanical defect. While it is always my responsibility as the Captain to do so; I had assumed that Dispatch; Maintenance; and the First Officer had all looked at the MEL carefully and that just wasn't the case. Additionally; the Pitot Light Checklist notes say to avoid icing conditions so I was lulled into thinking that we had already adequately addressed that concern and were in full compliance with the MEL. It was only enroute when we discovered Proviso B was I reminded that in-flight notes and cautions are an entirely different animal from MEL requirements.  While the weather enroute and at our alternate did not present any dangerous additive conditions; I certainly would have made the decision to taxi back to the gate and have the defect corrected. I thought our Crew coordination was working very well using the Volant model. Despite the additive conditions of addressing a MEL after pushback; I thought the communication between the Crew and all external agencies was fluid; agreeable; and in compliance with procedures. Never once were we 'in the Red' because our training; checklists; and procedures kept the situation well within the realm of normal line duties. It was only after the situation had been fully addressed and documented did the error occur. We were in the Green; or so we thought; and completely comfortable with continuing the mission under the new plan. In hindsight; there was a breakdown among four different entities (Dispatch; Maintenance; Pilot Flying; and Pilot Monitoring); any one of whom could have broken the chain in this event and recommended a more desirable outcome; specifically; return to the gate. Ultimately; I am the Captain of the aircraft and I assume full responsibility for overlooking this proviso. In the future; I will never let perceived time constraints preclude me from taking the performance manual and going over all pertinent information while I still have Dispatch and Maintenance on the phone. I would advise all other groups in the decision chain to do the same.


Second narrative: [Report narrative contained no additional information].


Synopsis: During taxi for takeoff a B737-700 the Captain's PITOT HT light illuminated so maintenance MEL'ed it before takeoff. Everyone missed the MEL statement dispatchable for 'day VMC' only so the flight diverted to an enroute airport for maintenance.