Oilheat Efficiency, Renewable Fuel Research and Jobs Training Act of 2013

Oilheat Efficiency, Renewable Fuel Research and Jobs Training Act of 2013 - Amends the National Oilheat Research Alliance Act of 2000 to: (1) require the National Oilheat Research Alliance to provide the Secretary of Energy (DOE) with a list of qualified nominees for Alliance membership, and (2) revise membership criteria.

Includes among Alliance functions research to: (1) develop renewable fuels; and (2) examine the compatibility of different renewable fuels with oilheat fuel utilization equipment, with priority given to research on the development and use of advanced biofuels.

Changes the Alliance's proposed budget from annual to biennial.

Limits the current assessment rate of 2/10 of 1 cent per gallon of oilheat fuel (currently, of No. 1 distillate and No. 2 dyed distillate) to calendar years 2013 and 2014.

Requires subsequent annual assessment rates to be sufficient to cover the costs of Alliance plans and programs. Limits those assessments, however, to a change of no more than 1/2 of 1 cent per gallon of oilheat fuel.

Prohibits any assessment increase unless: (1) it is approved by 3/4 of Alliance members voting at a regularly scheduled meeting, and (2) the Alliance notifies certain congressional committees of the proposed increase at least 90 days before the meeting.

Prohibits such assessments from being passed through to, or otherwise required to be paid by, residential consumers of oilheat fuel.

Requires a qualified state association to deposit funds received under this Act in an account separate from its other funds.

Directs the Alliance to ensure that specified percentages of assessments collected for each calendar year are used by qualified state associations or the Alliance to: (1) conduct research, development, and demonstration activities relating to oilheat fuel, including development of energy-efficient heating and the transition and facilitation of the entry of energy-efficient heating systems into the marketplace; and (2) develop consumer education materials.

Directs the Alliance to require that at least 20% of the demonstration cost or commercial application program be provided by a source other than the Alliance.

Directs the Alliance to ensure that heating system conversion assistance is coordinated with administrators of a specified low-income home energy assistance program and with the Weatherization Assistance Program for Low-Income Persons.

Repeals: (1) the requirement for an annual analysis of oilheat price changes relative to other energy sources (market survey); as well as (2) the restriction of Association activities to research and development, training, and safety matters if in any year the five-year average price composite index of consumer grade oilheat exceeds a certain amount.

Prohibits the use of funds derived from assessments collected by the Alliance for lobbying purposes.

Directs the Secretary of Commerce, in the event of noncompliance with this Act by the Alliance, a qualified state association, or any other person or entity, to notify Congress and the Alliance website.

Extends the sunset date for the National Oilheat Research Alliance program to 19 years after the date on which it was established.