A system comprising: an ablation catheter comprising an elongate body having a plurality of temperature-measurement devices distributed along a distal end portion of the elongate body; an energy source configured to apply ablative energy sufficient to ablate target tissue to at least one energy delivery member (3130, 3135) positioned along the distal end portion of the elongate body; and at least one processing device configured to, upon execution of specific instructions stored on a computer-readable medium: obtain temperature measurements from each of the plurality of temperature-measurement devices at a plurality of time points; at each time point, determine a time-based characteristic of a temperature response for each of the plurality of temperature-measurement devices from the obtained temperature measurements; at each time point, apply a moving average to the obtained temperature measurements to filter noise and subtract a starting temperature value from the moving average to determine a temperature rise value; at each time point, determine an orientation of the distal end of the elongate body relative to the tissue from one of a plurality of orientation options based, at least in part, on a comparison of the time-based characteristics of the temperature responses for at least two of the plurality of temperature-measurement devices, and on the determined temperature rise values, wherein the plurality of orientation options consists of a parallel orientation, a perpendicular orientation and an oblique orientation; and display the determined orientation of the distal end of the elongate body, the displaying including one or more graphical images indicating the plurality of orientation options. an ablation catheter comprising an elongate body having a plurality of temperature-measurement devices distributed along a distal end portion of the elongate body; an energy source configured to apply ablative energy sufficient to ablate target tissue to at least one energy delivery member (3130, 3135) positioned along the distal end portion of the elongate body; and at least one processing device configured to, upon execution of specific instructions stored on a computer-readable medium: obtain temperature measurements from each of the plurality of temperature-measurement devices at a plurality of time points; at each time point, determine a time-based characteristic of a temperature response for each of the plurality of temperature-measurement devices from the obtained temperature measurements; at each time point, apply a moving average to the obtained temperature measurements to filter noise and subtract a starting temperature value from the moving average to determine a temperature rise value; at each time point, determine an orientation of the distal end of the elongate body relative to the tissue from one of a plurality of orientation options based, at least in part, on a comparison of the time-based characteristics of the temperature responses for at least two of the plurality of temperature-measurement devices, and on the determined temperature rise values, wherein the plurality of orientation options consists of a parallel orientation, a perpendicular orientation and an oblique orientation; and display the determined orientation of the distal end of the elongate body, the displaying including one or more graphical images indicating the plurality of orientation options. obtain temperature measurements from each of the plurality of temperature-measurement devices at a plurality of time points; at each time point, determine a time-based characteristic of a temperature response for each of the plurality of temperature-measurement devices from the obtained temperature measurements; at each time point, apply a moving average to the obtained temperature measurements to filter noise and subtract a starting temperature value from the moving average to determine a temperature rise value; at each time point, determine an orientation of the distal end of the elongate body relative to the tissue from one of a plurality of orientation options based, at least in part, on a comparison of the time-based characteristics of the temperature responses for at least two of the plurality of temperature-measurement devices, and on the determined temperature rise values, wherein the plurality of orientation options consists of a parallel orientation, a perpendicular orientation and an oblique orientation; and display the determined orientation of the distal end of the elongate body, the displaying including one or more graphical images indicating the plurality of orientation options.