The quick answer is: results may vary. To the extent that temperature regime changes in a given location, and the product in question is tempertaure regime sensitive (most are not very), then yes. There may be more of an effect from changes in precipitation, with areas experiencing increased ppt seeing some minor impact.

The larger impact will be on the pest and diseases themselves - a changed climate in a goven area will mean better or worse conditions for the suite of pests and diseases already rpesetn there, and for possible invaders. So it is not so much that the plant proteciton products will become more or less effective, as it is that the pests and diseases they are used to protect against will become more or less agressive and may change.

This is a location-dependant perspective; on a broader non-locational perspective, there should be no hnage in the effectiveness of the products, but there may be a change in which products need to be deployed where.

For biopesticides that have activity via volatility (eg attractants, repellents) then temperature and humidity can have an effect. We see this regularly when we test biopesticides on raspberries in polytunnels and in open fields. 

We also see that plant stress (eg drought) can affect the level of resistance or susceptibility to pests and diseases. Plants seem able to switch resources depending on current stressors (type and severity) so there are strong genotype x environment interactions. we saw this in our EU PURE project, testing tomato genotypes with several primers and elicitors to induce resistance to Botrytis and root know nematodes (paper currently under review for a special edition of  Crop Protection).

Acoording to Jørgen E. Olesen and  Marco Bindi (2002) in an article that you will find on research gate the authors maintain that  'conditions are more favourable for the proliferation

of insect pests in warmer climates, because many insects can then complete a greater number of reproductive cycles (Cammel and Knight,

1992).

The authors have an extensive bibliography that is very useful.

see https://www.researchgate.net/profile/Jorgen_Olesen2/publication/222403222_Consequences_of_climate_change_for_European_agricultural_productivity_land_use_and_policy/links/0fcfd50a940dfe4d47000000.pdf

I observed some of the effects of  increased humidity or drought on the crops grown in Danube floodplain. In an ethnographic study I conducted respondents confirmed all the problems that the two above authors discuss.

Article Consequences of climate change for European agricultural pro...