Someone have ad this problem , the engine hesitate at 1/4 throttle but only when engine is cold (for the first 2 or 3 minute of ride when engine is cold ) look like fuel delivery problem ,
does the water temp sensor did something with fuel delivery ?

if it was map or iat sensor , he would hesitate when he is hot too ?

What machine? Year and size.

Brute force 750 2012 eps fuel injected

Sounds lean when cold but not so when hot. Might test a few things like that map sensor, the TPC and the idle air valve. Also look for something physical like a cracked TB boot. I would also test the fuel pressure.

Tb boot are good
I dont have thinking about the IAV who can stay open .
Fuel pump mod have been done 2 year ago ,
destruction of screen in fuel pump assembly new strainer and inline filter , but if it was fuel pump the problem will be more at wot throttle , than at 1/4 throttle .
I have put a wideband on the past , to set the afr with a hmf fuel optimizer and this bike run realy rich , but i dont know what is the normal AFR mapping ?