as Al mentioned higher heat input will achieve slow the rate of cooling and increase grain size etc. This can also be achieved by using a preheat and not changing the welding parameters.
BUT I should mention that increasing all three: high voltages, amps AND travel speed won't neccessarily increase heat input. for 2 reasons:
The real formula you are looking for is kiloJoules/inch or another measure of heat input per inch. this formula is found by taking Volts X Amps X 60 / (Travel speed in Inches per minute) It leaves you with a Joules/Inch
Now I mention this because sometimes significantly increasing voltage and amperage means welders will naturally OVER compensate and run faster actually reducing heat input per unit which is normally desired, unless of course you want slower cooling. I included the formula in my welding cost estimator
http://www.aws.org/cgi-bin/mwf/topic_show.pl?pid=105308;hl=calculator because all the relevant data was already there. You can play around with it and see what comes up.
The second is a concept of heat conduction theory in that it is exponentially related to the velocity of a moving heat source. In other words a heat source moving twice as fast will have to put in much more than double the energy in order for the material to conduct the same amount of heat away from the source. Conduction is a function of time and if the heat source is only applied momentarily (as it is in welding) the heat affected zone will only grow so wide. This is why you can quickly move your finger through a candle or flame without even feeling it. Most welders will realize this too in welding something like stainless steel that's sensitive to over heating. If you run tiny little stringer beads and go too slow your welds will almost always oxidize too much.
I wish I could remember the formula Stephan or Crisi posted it a year or so ago.
Anyways those 2 concepts work in conjunction. Generally the second one is left out unless we are talking about significant changes in welding speed.