The bulk of this episode is based on the UK NICE guideline: Feverish illness in children under 5, published in 2013. http://guidance.nice.org.uk/CG160

The guideline covers:

Thermometers and the detection of fever
Clinical assessment of the child with fever (using the traffic light system)
Management by remote assessment
Management by the non-paediatric practitioner
Management by the paediatric specialist (investigations summarized below)
Antipyretic interventions

The Traffic Light System in assessing risk for serious infection
This assessment tool takes into consideration color/appearance, activity, respiratory, circulation and hydration, and "other" parameters. For each parameter, their associated signs and symptoms are assigned a color code: "green" (low risk), "amber" (intermediate risk) and "red" (high risk). The table can be found here.
Age-appropriate investigations for pediatric fever
Once the risk for serious infection is determined, the following investigation should be performed:

Age
CBC diff
BC
CRP
UA/UC
LP
CXR
Stool culture

15 or =3mo, RED
yes
yes
yes
yes
yes
yes
if indicated

>=3mo, AMBER
yes
yes
yes
yes
if 39 and WBC >20
if indicated

>=3mo, GREEN
no
no
no
yes
no
no
if indicated

And at the same time, empiric parenteral antibiotic coverage for meningitis (3rd generation cephalosporin plus ampicillin/amoxicillin) should be started if LP is indicated.