How does the speed of the particles of a gas change when the gas is heated?

I hope you can understand this and i hope this helps.
 Speed increases with increasing temperature. Gas molecule speed follows the formula 
v(average) = 8RT/(pi*M), where 
M = molar mass (e.g., 0.002 kg/mole for hydrogen) 
R = universal gas constant = 8.314472 J/(mole-degK) 
T = temperature K 
The ref. gives the derivation of this formula and other formulas for v(RMS) and v(most probable).If u dont understand i can make it simpler just ask.

If the water vapor content stays the same and the temperature drops, then the relative humidity increases. its vise versa.if the water vapor content stats the same and the temperature rises, the relative humidity decreases. so, yes, i'd say that temperature and humidity have a strong relationship.