Blackbody to SRGB code based on piecewise blackbody curve reconstruction. Depends on XPL, but you can easily replace its vector-construction calls in blackbody_rgbi and blackbody_rgb with your own.

blackbody_srgb.c

// science/blackbody_srgb.c. ©2014 Informi Software Inc. Use and modify this file for any purpose without attribution.

#include "science/blackbody_srgb.h"

#ifndef XPL_STATIC_INLINE
#	define XPL_STATIC_INLINE static inline
#endif

XPL_STATIC_INLINE float r_0_6700(float k) {
	return 1.0f;
}

XPL_STATIC_INLINE float r_6700_10000(float k) {
	return 6380.0f / k;
}

XPL_STATIC_INLINE float r_10000(float k) {
	return 0.313f * k / (k - 5100.0f);
}

XPL_STATIC_INLINE float g_0_1100(float k) {
	return 0.000005f * k;
}

XPL_STATIC_INLINE float g_1100_4000(float k) {
	return 0.000204f * k - 0.164f;
}

XPL_STATIC_INLINE float g_4000_6700(float k) {
	return -2956.0f / k + 1.39f;
}

XPL_STATIC_INLINE float g_6700_10000(float k) {
	return 5030.0f / k + 0.196f;
}

XPL_STATIC_INLINE float g_10000(float k) {
	return 0.436f * k / (k - 3820.0f) - 0.0006f;
}

XPL_STATIC_INLINE float b_0_2086(float k) {
	return 0.0f;
}

XPL_STATIC_INLINE float b_2086_4000(float k) {
	return 0.00018f * k - 0.378f;
}

XPL_STATIC_INLINE float b_4000_6700(float k) {
	return 0.000245f * k - 0.64f;
}

XPL_STATIC_INLINE float b_6700(float k) {
	return 1.0f;
}

XPL_STATIC_INLINE float i_0_15000(float k) {
	return (k == 0.f) ? 0.f : 179.3f * powf(k, (-3509.0f / (k + 0.001f)));
}

XPL_STATIC_INLINE float i_15000(float k) {
	return 0.00313f * k - 28.04f;
}

xvec4 blackbody_rgbi(float k) {
	if (k <= 1100.0f) return xvec4_set(r_0_6700(k), g_0_1100(k), b_0_2086(k), i_0_15000(k));
	if (k <= 2086.0f) return xvec4_set(r_0_6700(k), g_1100_4000(k), b_0_2086(k), i_0_15000(k));
	if (k <= 4000.0f) return xvec4_set(r_0_6700(k), g_1100_4000(k), b_2086_4000(k), i_0_15000(k));
	if (k <= 6700.0f) return xvec4_set(r_0_6700(k), g_4000_6700(k), b_4000_6700(k), i_0_15000(k));
	if (k <= 10000.0f) return xvec4_set(r_6700_10000(k), g_6700_10000(k), b_6700(k), i_0_15000(k));
	if (k <= 15000.0f) return xvec4_set(r_10000(k), g_10000(k), b_6700(k), i_0_15000(k));
	return xvec4_set(r_10000(k), g_10000(k), b_6700(k), i_15000(k));
}

xvec3 blackbody_rgb(float k) {
	if (k <= 1100.0f) return xvec3_set(r_0_6700(k), g_0_1100(k), b_0_2086(k));
	if (k <= 2086.0f) return xvec3_set(r_0_6700(k), g_1100_4000(k), b_0_2086(k));
	if (k <= 4000.0f) return xvec3_set(r_0_6700(k), g_1100_4000(k), b_2086_4000(k));
	if (k <= 6700.0f) return xvec3_set(r_0_6700(k), g_4000_6700(k), b_4000_6700(k));
	if (k <= 10000.0f) return xvec3_set(r_6700_10000(k), g_6700_10000(k), b_6700(k));
	if (k <= 15000.0f) return xvec3_set(r_10000(k), g_10000(k), b_6700(k));
	return xvec3_set(r_10000(k), g_10000(k), b_6700(k));
}

blackbody_srgb.h

#ifndef p1_blackbody_srgb_h
#define p1_blackbody_srgb_h

#include <xpl/math/vec4.h>
#include <xpl/math/vec3.h>

xvec4 blackbody_rgbi(float kelvin);
xvec3 blackbody_rgb(float kelvin);

#endif