The only set of charts to which I have regular access are those in the CAP 698 which is published by the CAA for use in JAR ATPL exams. These are reputedly based on a version of the 737, but I know not which.
The engines used in these charts are flat rated up to ISA +15 degrees C. The climb performance charts show a steady decline in climb performance at any given altitude up to the flat rating temperature limit. This is followed by an abrupt increase in performance degradation at higher temperatures. The overall implication of this being that flat rating reduces the detrimental effects of increasing temperatures, but does not entirely eliminate these effects.
If we ignore flat rating to simplify the arguments we will see that increasing temperature has two effects. These are a decrease in power available and an increase in power required. The overall result of increasing ambient temperature is therefore a reduction in excess power and hence a reduction in best possible ROC.
The principal cause of the reduction in power availabe is the reduction in thrust. In a non-flat rated engine the thrust reduction is caused by a reduction in mass flow due to reduced air density. In a flat rated engine it is caused by the reduced acceleration of the air, which is in turn caused by the increased TAS to CAS ratio.
The principal cause of the increase in power required is the increase in TAS at any given CAS. Power required is equal to drag x TAS. If we assume that drag at any given CAS remains constant, then the power required is proportional to any temperature-induced change in TAS.
The drag equation includes TAS squared, so multiplying drag by TAS to get power required, gives something that is proportional to TAS cubed. So any increase in TAS at any given CAS will cause an even bigger increase in power required.
To visualise the effects of temperature we need to sketch power required and power available curves. Power required looks like a drag curve which has been rotated in an anti-clockwise direction..A bit like a NIKE tick.
For a jet aircraft if we simplify the situation by assuming that thrust is constant at all values of TAS, the power available is a straight line starting at the origin (0,0) and moving up towards the top right hand corner of the chart. At low altitude these two lines will cross at two points. At these crossing points the power available is equal to the power required. At all higher and lower speeds the power available is less than the power required. So these two points are the minimum and maximum speeds for which sufficient power is available.
At all speeds between the two crossing points the power available is greater than the power required. This excess power can be used to provide a rate of climb. The excess power and hence ROC are proportional to the vertical distance between the two power curves. ROC will be greatest at the speed at which the vertical distance between the two lines is greatest.
If we draw a tangent from the origin to touch the under surface of the power available curve we can use this to predict the effects of changes in altitude or temperature. All subsequent power available curves are similar to the first and all curves touch the same tangent. Increasing altitude or increasing temperature cause the power required curve to slide up the tangent towards the right hand end of the chart.
The power available curve always starts at the origin because at this point it is equal to thrust multiplied by zero TAS. Its angle is dependent upon altitude and temperature. Increasing altitude and increasing temperarture both cause this curve to rotate clockwise about the origin, thereby reducing power available at any given TAS.
The overall effect of these changes is that increasing altitude or increasing temperature will increase power required, reduce power available and reduce ROC.
The use of flat rated engines reduces the rate of reduction in power available but has no effect on the rate of increase in the power required.