99°F-109°F doesn't sound so bad. Its a dry heat right?
don't know your past history of this 85 K100 other then the engine swap

1) Do you have the 'vacuum or pressure switch' found mounted on the back of the throttle bodies
If present unplug and tape connector somewhere to harness
Plug port on throttle bodies #1
No longer needed
http://www.motobrick.com/index.php?topic=8494.0https://www.k100-forum.com/t15097-what-is-this2) Is the fuel pressure regulator connected properly?
check hoses to the Fuel Pressure Regulator found mounted behind the throttle bodies
1-vacuum hose from throttle bodies to the bottom FPR
2-middle hose from petrol fuel injection fuel rail
3-top hose to petrol tank return line

3) need to ensure the tank venting is working properly not obstructed, discharge hoses are connected or "Air Accumulator Cup" is present & hose connected to it routed down the backside of right footpeg plate
possibly have the emissions check valve on the tank vent port/hose which is no longer needed and the engine block may or may not have the tubing/stud port circled below
Picture below you may remove/omit the tubing and gray check valve and cap off the tubing nipple/stub on the front of the block under the radiator shroud.
Or leave rubber tubing and gray check valve in place and disconnect from tank vent and plug rubber tubing with a bolt or suitable hardware.
This was BMW evapoative emission compliance of the time but later removed.


Service Bulletin 2228
http://www.motobrick.com/index.php/topic,4984.0.htmlDuring moto use its possible for petrol and fumes to be expelled from tank especially when full. Sloshing petrol can be sucked up into the tubing vent and expelled under tank pressure.
Exterior petrol tank bottom has 2 tubing nipple piped into the tank for petrol fume vent and the water/rain drain collected from around petrol gas cap.
K100 may or may not have the air accumulator cup 16132307467 installed to collect any expelled petrol or water from tank nipples with 1 rubber hose connected and routed down
to lower right footpeg plate.
Or instead 2 rubber hoses will be connected direct to the petrol tank tubing nipples if there is no air accumulator cup. Again hoses routed down to lower right footpeg plate.
The hole at 6:30 is the water drain. The notch in the petrol tank cap has to line up to that hole. The indicated tubing is the tank vent.

1985 K100 petrol tank bottom
forward tubing/stub is tank vent
rear tubing/stub- petrol cap rain drain

AIR ACCUMULATOR

AIR ACCUMULATOR LOCATION